Edit Profile (opens in new tab) Gunzburger, Max D. Co-Author Distance Author ID: gunzburger.max-d Published as: Gunzburger, Max; Gunzburger, Max D.; Gunzburger, M. D.; Gunzburger, M. more...less External Links: MGP · Wikidata · Math-Net.Ru · dblp · IdRef Documents Indexed: 330 Publications since 1970, including 3 Books and 8 Additional arXiv Preprints 10 Contributions as Editor Biographic References: 3 Publications Co-Authors: 167 Co-Authors with 322 Joint Publications 4,260 Co-Co-Authors all top 5 Co-Authors 15 single-authored 37 Du, Qiang 33 Bochev, Pavel B. 29 Peterson, Janet S. 25 Ju, Lili 16 Nicolaides, Roy A. 15 Burkardt, John V. 14 D’Elia, Marta 13 Lee, Hyung-Chun 12 Lehoucq, Richard B. 12 Wang, Xiaoming 10 Cao, Yanzhao 10 Hou, L. Steven 10 Manservisi, Sandro 10 Webster, Clayton G. 10 Zhang, Guannan 9 Fix, George J. 9 Wang, Zhu 8 Svobodny, Thomas P. 7 Fursikov, Andreĭ Vladimirovich 7 Guan, Qingguang 7 Parks, Michael L. 6 Capodaglio, Giacomo 6 Perego, Mauro 6 Schneier, Michael 5 Chen, Qingshan 5 Cheung, James 5 Hou, Lisheng 5 Jiang, Nan 5 Lee, Eunjung 5 Trenchea, Catalin 5 Wang, Jilu 5 Zhao, Wenju 4 Badia, Santiago 4 Chapman, Stephen Jonathan 4 Chen, Wenbin 4 Gruber, Anthony 4 Hua, Fei 4 Lee, Hyesuk Kwon 4 Li, Buyang 4 Ming, Ju 4 Ringler, Todd D. 4 Saka, Yuki 4 Seleson, Pablo 4 Shadid, John N. 4 Vollmann, Christian 4 Willcox, Karen E. 4 Wood, Houston G. III 4 Zhao, Weidong 3 Alali, Bacim 3 Burkhardt, John 3 Burkovska, Olena 3 Cliff, Eugene M. 3 Deang, Jennifer M. 3 He, Xiaoming 3 Iliescu, Traian 3 Kim, Hongchul 3 Kunoth, Angela 3 Lan, Rihui 3 Lee, Jeehyun 3 Leng, Wei 3 Liu, Chen-Huei 3 Peherstorfer, Benjamin 3 Turner, James C. jun. 3 Wang, Xiaoqiang 3 Xu, Feifei 3 Zhang, Xiaoping 3 Zhang, Yanzhi 3 Zhou, Kun 3 Zhu, Wenxiang 2 Burns, John A. 2 Calhoun-Lopez, Marcus 2 Chang, Ching Lung 2 Chen, Zheng 2 Choi, Jungmin 2 Gottlieb, David I. 2 Gu, Rui 2 Jordan, Jo Ann 2 Klar, Manuel 2 Layton, William J. 2 Liu, Kuo 2 Mohebujjaman, Muhammad 2 Pieper, Konstantin 2 Rozza, Gianluigi 2 Sun, Dong 2 Teckentrup, Aretha L. 2 Tian, Xiaochuan 2 Ting, Lu 2 Turkel, Eli L. 2 Wu, Xiaonan 2 Yang, Huanhuan 2 Yang, Sung-Dae 1 Alla, Alessandro 1 Appel, Justin R. 1 Barth, Teri L. 1 Bayliss, Alvin 1 Bertagna, Luca 1 Borggaard, Jeff T. 1 Borggaard, Jeffrey T. 1 Bornia, Giorgio 1 Calandrini, Sara ...and 68 more Co-Authors all top 5 Serials 26 Computer Methods in Applied Mechanics and Engineering 24 SIAM Journal on Numerical Analysis 22 Computers & Mathematics with Applications 11 Journal of Computational Physics 10 SIAM Journal on Control and Optimization 10 SIAM Journal on Scientific Computing 9 Journal of Mathematical Analysis and Applications 9 Numerische Mathematik 8 Mathematics of Computation 6 SIAM Review 6 Communications in Computational Physics 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Applied Mathematics and Computation 5 Journal of Computational and Applied Mathematics 5 Numerical Methods for Partial Differential Equations 5 Multiscale Modeling & Simulation 5 International Journal of Numerical Analysis and Modeling 5 Numerical Mathematics: Theory, Methods and Applications 5 SIAM/ASA Journal on Uncertainty Quantification 4 Computers and Fluids 4 Applied Mathematics Letters 4 Journal of Scientific Computing 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 AIAA Journal 3 International Journal for Numerical Methods in Fluids 3 International Journal of Computer Mathematics 3 Linear Algebra and its Applications 3 SIAM Journal on Applied Mathematics 3 International Journal of Computational Fluid Dynamics 3 Journal of Mathematical Fluid Mechanics 2 IMA Journal of Numerical Analysis 2 Journal of Applied Mechanics 2 Journal of Engineering Mathematics 2 Journal of Fluid Mechanics 2 Applied Mathematics and Optimization 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 SIAM Journal on Scientific and Statistical Computing 2 Journal of Computational Mathematics 2 Physica D 2 Applied Numerical Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Journal of Elasticity 2 SIAM Journal on Mathematical Analysis 2 Journal of Mathematical Imaging and Vision 2 Advances in Computational Mathematics 2 Discrete and Continuous Dynamical Systems. Series B 2 Computational Methods in Applied Mathematics 2 Acta Numerica 2 Oberwolfach Reports 2 International Journal for Uncertainty Quantification 1 Journal of Mathematical Biology 1 Journal of Sound and Vibration 1 Mathematical Methods in the Applied Sciences 1 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 1 International Journal for Numerical Methods in Engineering 1 Kyungpook Mathematical Journal 1 Transactions of the American Mathematical Society 1 Optimal Control Applications & Methods 1 Chinese Annals of Mathematics. Series B 1 Parallel Computing 1 European Journal of Applied Mathematics 1 Computational Geometry 1 Numerical Algorithms 1 Advances in Mathematical Sciences and Applications 1 Zapiski Nauchnykh Seminarov POMI 1 Communications in Numerical Methods in Engineering 1 Methods and Applications of Analysis 1 Discrete and Continuous Dynamical Systems 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 Vietnam Journal of Mathematics 1 Fractional Calculus & Applied Analysis 1 Philosophical Transactions of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Flow, Turbulence and Combustion 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 International Journal of Pure and Applied Mathematics 1 Communications in Mathematical Sciences 1 Analysis and Applications (Singapore) 1 Applied Mathematical Sciences 1 The IMA Volumes in Mathematics and its Applications 1 Progress in Systems and Control Theory 1 Lecture Notes in Computational Science and Engineering 1 Advances in Design and Control 1 Results in Applied Mathematics all top 5 Fields 210 Numerical analysis (65-XX) 161 Fluid mechanics (76-XX) 143 Partial differential equations (35-XX) 58 Calculus of variations and optimal control; optimization (49-XX) 26 Mechanics of deformable solids (74-XX) 23 Probability theory and stochastic processes (60-XX) 19 Statistical mechanics, structure of matter (82-XX) 19 Systems theory; control (93-XX) 12 Integral equations (45-XX) 11 General and overarching topics; collections (00-XX) 11 Statistics (62-XX) 10 Geophysics (86-XX) 8 Mechanics of particles and systems (70-XX) 6 Real functions (26-XX) 5 Computer science (68-XX) 5 Optics, electromagnetic theory (78-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Operations research, mathematical programming (90-XX) 4 Biology and other natural sciences (92-XX) 3 Ordinary differential equations (34-XX) 3 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 292 Publications have been cited 7,845 times in 4,816 Documents Cited by ▼ Year ▼ Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 327 2012 Centroidal Voronoi tessellations: Applications and algorithms. Zbl 0983.65021 Du, Qiang; Faber, Vance; Gunzburger, Max 286 1999 Perspectives in flow control and optimization. Zbl 1088.93001 Gunzburger, Max D. 247 2003 Stabilization of low-order mixed finite elements for the Stokes equations. Zbl 1145.76015 Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D. 244 2006 Finite element methods for viscous incompressible flows. Zbl 0697.76031 Gunzburger, Max D. 236 1989 A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 221 2013 Least-squares finite element methods. Zbl 1168.65067 Bochev, Pavel B.; Gunzburger, Max D. 216 2009 On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics. Zbl 0731.76094 Gunzburger, Max D.; Meir, Amnon J.; Peterson, Janet S. 197 1991 Boundary conditions for the numerical solution of elliptic equations in exterior regions. Zbl 0479.65056 Bayliss, Alvin; Gunzburger, Max; Turkel, Eli 171 1982 Analysis and approximation of the Ginzburg-Landau model of superconductivity. Zbl 0787.65091 Du, Qiang; Gunzburger, Max D.; Peterson, Janet S. 162 1992 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 148 2018 Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. Zbl 1189.35244 Cao, Yanzhao; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 132 2010 Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. Zbl 1252.76040 Cao, Yanzhao; Gunzburger, Max; Hu, Xiaolong; Hua, Fei; Wang, Xiaoming; Zhao, Weidong 125 2010 Finite element methods of least-squares type. Zbl 0914.65108 Bochev, Pavel B.; Gunzburger, Max D. 124 1998 The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. Zbl 1345.35128 D’Elia, Marta; Gunzburger, Max 121 2013 Stochastic finite element methods for partial differential equations with random input data. Zbl 1398.65299 Gunzburger, Max D.; Webster, Clayton G.; Zhang, Guannan 106 2014 Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems. Zbl 1457.65089 Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 101 2014 A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. Zbl 1414.76017 Chen, Wenbin; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 96 2011 A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057 Gunzburger, Max; Lehoucq, R. B. 94 2010 Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Zbl 1225.74082 Chen, X.; Gunzburger, Max 94 2011 POD and CVT-based reduced-order modeling of Navier-Stokes flows. Zbl 1120.76323 Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun 92 2006 Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Zbl 1305.76072 Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 90 2011 Analysis of a linear fluid-structure interaction problem. Zbl 1039.35076 Du, Qiang; Gunzburger, M. D.; Hou, L. S.; Lee, J. 80 2003 Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. Zbl 0970.35096 Gunzburger, Max D.; Lee, Hyung-Chun; Seregin, Gregory A. 79 2000 Numerical methods for nonlocal and fractional models. Zbl 07674560 D’Elia, Marta; Du, Qiang; Glusa, Christian; Gunzburger, Max; Tian, Xiaochuan; Zhou, Zhi 78 2020 Efficient and long-time accurate second-order methods for the Stokes-Darcy system. Zbl 1282.76094 Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 68 2013 Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. Zbl 0963.35150 Gunzburger, M. D.; Manservisi, S. 67 2000 Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. Zbl 1121.65354 Gunzburger, Max D.; Peterson, Janet S.; Shadid, John N. 67 2007 Boundary velocity control of incompressible flow with an application to viscous drag reduction. Zbl 0756.49004 Gunzburger, Max D.; Hou, Lisheng; Svobodny, Thomas P. 66 1992 Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. Zbl 0737.76045 Gunzburger, M. D.; Hou, L. S.; Svobodny, Th. P. 63 1991 Finite-dimensional approximation of a class of constrained nonlinear optimal control problems. Zbl 0849.49005 Gunzburger, Max D.; Hou, L. Steven 61 1996 Analysis of least squares finite element methods for the Stokes equations. Zbl 0816.65082 Bochev, Pavel B.; Gunzburger, Max D. 60 1994 Fractional diffusion on bounded domains. Zbl 1488.35557 Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M. 59 2015 Peridynamics as an upscaling of molecular dynamics. Zbl 1375.82073 Seleson, Pablo; Parks, Michael L.; Gunzburger, Max; Lehoucq, Richard B. 59 2009 A multilevel stochastic collocation method for partial differential equations with random input data. Zbl 1327.65014 Teckentrup, A. L.; Jantsch, P.; Webster, C. G.; Gunzburger, M. 56 2015 Constrained centroidal Voronoi tessellations for surfaces. Zbl 1036.65101 Du, Qiang; Gunzburger, Max D.; Ju, Lili 55 2003 A taxonomy of consistently stabilized finite element methods for the Stokes problem. Zbl 1133.76307 Barth, Teri; Bochev, Pavel; Gunzburger, Max; Shadid, John 53 2004 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 51 2016 The velocity tracking problem for Navier-Stokes flows with bounded distributed controls. Zbl 0938.35118 Gunzburger, M. D.; Manservisi, S. 50 1999 Issues related to least-squares finite element methods for the Stokes equations. Zbl 0953.65083 Deang, Jennifer M.; Gunzburger, Max D. 49 1999 Least-squares methods for the velocity-pressure-stress formulation of the Stokes equations. Zbl 1067.76562 Bochev, Pavel B.; Gunzburger, Max D. 48 1995 Analysis of a Ladyzhenskaya model for incompressible viscous flow. Zbl 0712.76039 Du, Qiang; Gunzburger, Max D. 47 1991 Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls. Zbl 0747.76063 Gunzburger, M. D.; Hou, L.; Svobodny, T. P. 46 1991 The velocity tracking problem for Navier-Stokes flows with boundary control. Zbl 0991.49002 Gunzburger, M. D.; Manservisi, S. 45 2000 Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Zbl 1286.74010 Seleson, Pablo; Gunzburger, Max; Parks, Michael L. 45 2013 An ensemble-proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1394.76067 Gunzburger, Max; Jiang, Nan; Schneier, Michael 44 2017 Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Zbl 1173.74303 Fish, Jacob; Nuggehally, Mohan A.; Shephard, Mark S.; Picu, Catalin R.; Badia, Santiago; Parks, Michael L.; Gunzburger, Max 44 2007 Self-contained automated methodology for optimal flow control. Zbl 0901.76067 Joslin, Ronald D.; Gunzburger, Max D.; Nicolaides, Roy A.; Erlebacher, Gordon; Hussaini, M. Yousuff 41 1997 On atomistic-to-continuum coupling by blending. Zbl 1160.65338 Badia, Santiago; Parks, Michael; Bochev, Pavel; Gunzburger, Max; Lehoucq, Richard 40 2008 Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 40 2013 Grid generation and optimization based on centroidal Voronoi tessellations. Zbl 1024.65118 Du, Qiang; Gunzburger, Max 39 2002 Boundary value problems and optimal boundary control for the Navier-Stokes system: The two-dimensional case. Zbl 0910.76011 Fursikov, A. V.; Gunzburger, M. D.; Hou, L. S. 39 1998 An absolutely stable pressure-Poisson stabilized finite element method for the Stokes equations. Zbl 1159.76346 Bochev, Pavel; Gunzburger, Max 39 2004 On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equations. Zbl 1064.76118 Gunzburger, M. D.; Ladyzhenskaya, O. A.; Peterson, J. S. 39 2004 Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system. Zbl 1352.35093 Chen, Nan; Gunzburger, Max; Wang, Xiaoming 39 2010 Error estimates of stochastic optimal Neumann boundary control problems. Zbl 1243.65008 Gunzburger, Max D.; Lee, Hyung-Chun; Lee, Jangwoon 37 2011 Stability of the SUPG finite element method for transient advection-diffusion problems. Zbl 1067.76563 Bochev, Pavel B.; Gunzburger, Max D.; Shadid, John N. 34 2004 On stabilized finite element methods for the Stokes problem in the small time step limit. Zbl 1104.76059 Bochev, Pavel B.; Gunzburger, Max D.; Lehoucq, Richard B. 33 2007 Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes. Zbl 1436.35307 D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard 33 2017 On Stokes-Ritz projection and multistep backward differentiation schemes in decoupling the Stokes-Darcy model. Zbl 1465.65094 Gunzburger, Max; He, Xiaoming; Li, Buyang 33 2018 On finite element methods of the least squares type. Zbl 0422.65064 Fix, George J.; Gunzburger, Max D.; Nicolaides, R. A. 31 1979 Sensitivities, adjoints and flow optimization. Zbl 0962.76030 Gunzburger, Max D. 31 1999 Optimal boundary control for the evolutionary Navier-Stokes system: The three-dimensional case. Zbl 1076.76029 Fursikov, A. V.; Gunzburger, M. D.; Hou, L. S. 31 2005 An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system. Zbl 1388.76127 Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 31 2016 Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow. Zbl 0697.76046 Du, Qiang; Gunzburger, Max D. 31 1990 Accuracy of least-squares methods for the Navier–Stokes equations. Zbl 0779.76039 Bochev, Pavel B.; Gunzburger, Max D. 30 1993 On mixed finite element methods for first order elliptic systems. Zbl 0459.65072 Fix, G. J.; Gunzburger, M. D.; Nicolaides, R. A. 30 1981 An efficient algorithm for simulating ensembles of parameterized flow problems. Zbl 1466.65133 Gunzburger, Max; Jiang, Nan; Wang, Zhu 30 2019 Centroidal Voronoi tessellation-based reduced-order modeling of complex systems. Zbl 1111.65084 Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun 28 2006 Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Zbl 1014.68202 Ju, Lili; Du, Qiang; Gunzburger, Max 27 2002 Identification of the diffusion parameter in nonlocal steady diffusion problems. Zbl 1342.49053 D’Elia, M.; Gunzburger, M. 27 2016 Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032 Du, Qiang; Gunzburger, Max; Ju, Lili 27 2010 Adjoint equation-based methods for control problems in incompressible, viscous flows. Zbl 0996.76024 Gunzburger, Max 26 2000 An optimization-based domain decomposition method for the Navier-Stokes equations. Zbl 1003.76024 Gunzburger, Max D.; Lee, Hyesuk Kwon 26 2000 An optimization based domain decomposition method for partial differential equations. Zbl 0941.65123 Gunzburger, M. D.; Peterson, J. S.; Kwon, H. 26 1999 Incompressible computational fluid dynamics: trends and advances. Zbl 1190.76004 26 1993 Superconvergence analysis of FEMs for the Stokes-Darcy system. Zbl 1303.76086 Chen, Wenbin; Chen, Puying; Gunzburger, Max; Yan, Ningning 26 2010 Optimal distributed control of nonlocal steady diffusion problems. Zbl 1298.49006 D’Elia, Marta; Gunzburger, Max 26 2014 A Ginzburg-Landau type model of superconducting normal junctions including Josephson junctions. Zbl 0843.35120 Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D. 25 1995 Peridynamics and material interfaces. Zbl 1455.74009 Alali, Bacim; Gunzburger, Max 25 2015 A sparse-grid method for multi-dimensional backward stochastic differential equations. Zbl 1289.65011 Zhang, Guannan; Gunzburger, Max; Zhao, Weidong 25 2013 Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere. Zbl 1046.65094 Du, Qiang; Gunzburger, Max D.; Ju, Lili 24 2003 On inf–sup stabilized finite element methods for transient problems. Zbl 1079.76577 Bochev, Pavel B.; Gunzburger, Max D.; Shadid, John N. 24 2004 A locally conservative least-squares method for Darcy flows. Zbl 1191.76066 Bochev, P. B.; Gunzburger, M. D. 23 2008 Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data. Zbl 1260.65007 Zhang, Guannan; Gunzburger, Max 22 2012 A second-order time-stepping scheme for simulating ensembles of parameterized flow problems. Zbl 1421.76157 Gunzburger, Max; Jiang, Nan; Wang, Zhu 22 2019 Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise. Zbl 1418.60077 Gunzburger, Max; Li, Buyang; Wang, Jilu 21 2019 A model for variable thickness superconducting thin films. Zbl 0862.35119 Chapman, S. J.; Du, Qiang; Gunzburger, M. D. 21 1996 Semidiscrete finite element approximations of a linear fluid-structure interaction problem. Zbl 1159.74343 Du, Qiang; Gunzburger, M. D.; Hou, Lisheng; Lee, Jeehyun 21 2004 A finite element method for first order elliptic systems in three dimensions. Zbl 0631.65108 Chang, Ching-Lung; Gunzburger, Max D. 21 1987 Least-squares finite element approximations to solutions of interface problems. Zbl 0913.65096 Cao, Yanzhao; Gunzburger, Max D. 20 1998 On least squares approximations to indefinite problems of the mixed type. Zbl 0378.76046 Fix, George J.; Gunzburger, Max D. 20 1978 On least-squares finite element methods for the Poisson equation and their connection to the Dirichlet and Kelvin principles. Zbl 1128.76031 Bochev, Pavel; Gunzburger, Max 20 2005 Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi-Delaunay triangulations. Zbl 1126.65099 Ju, Lili; Gunzburger, Max; Zhao, Weidong 20 2006 Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses. Zbl 0748.76073 Gunzburger, Max D.; Hou, Steven L. 20 1992 Least-squares finite element methods. Zbl 1100.65098 Bochev, Pavel; Gunzburger, Max 19 2006 Analysis and discretization of an optimal control problem for the time-periodic MHD equations. Zbl 1073.49003 Gunzburger, Max; Trenchea, Catalin 19 2005 On conforming finite element methods for the inhomogeneous stationary Navier-Stokes equations. Zbl 0559.76026 Gunzburger, Max D.; Peterson, Janet S. 19 1983 On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072 Gottlieb, David; Gunzburger, Max; Turkel, Eli 19 1982 A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1402.35207 Gunzburger, Max; Jiang, Nan; Schneier, Michael 19 2018 Energetically consistent model reduction for metriplectic systems. Zbl 07644831 Gruber, Anthony; Gunzburger, Max; Ju, Lili; Wang, Zhu 1 2023 An asymptotically compatible coupling formulation for nonlocal interface problems with jumps. Zbl 07704386 Glusa, Christian; D’Elia, Marta; Capodaglio, Giacomo; Gunzburger, Max; Bochev, Pavel B. 1 2023 A comparison of neural network architectures for data-driven reduced-order modeling. Zbl 1507.65157 Gruber, Anthony; Gunzburger, Max; Ju, Lili; Wang, Zhu 6 2022 A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere. Zbl 1515.76096 Gunzburger, Max; Li, Buyang; Wang, Jilu; Yang, Zongze 2 2022 High-order multirate explicit time-stepping schemes for the baroclinic-barotropic split dynamics in primitive equations. Zbl 1515.76159 Lan, Rihui; Ju, Lili; Wang, Zhu; Gunzburger, Max; Jones, Philip 1 2022 A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems. Zbl 1473.65188 D’Elia, Marta; Gunzburger, Max; Vollmann, Christian 9 2021 On a nonlocal Cahn-Hilliard model permitting sharp interfaces. Zbl 1484.35352 Burkovska, Olena; Gunzburger, Max 8 2021 A multifidelity method for a nonlocal diffusion model. Zbl 1524.35206 Khodabakhshi, Parisa; Willcox, Karen E.; Gunzburger, Max 3 2021 Parallel exponential time differencing methods for geophysical flow simulations. Zbl 1507.76236 Lan, Rihui; Leng, Wei; Wang, Zhu; Ju, Lili; Gunzburger, Max 2 2021 Nonlinear level set learning for function approximation on sparse data with applications to parametric differential equations. Zbl 1499.65052 Gruber, Anthony; Gunzburger, Max; Ju, Lili; Teng, Yuankai; Wang, Zhu 1 2021 Approximation of probability density functions for PDEs with random parameters using truncated series expansions. Zbl 1471.62309 Capodaglio, Giacomo; Gunzburger, Max; Wynn, Henry P. 1 2021 Numerical methods for nonlocal and fractional models. Zbl 07674560 D’Elia, Marta; Du, Qiang; Glusa, Christian; Gunzburger, Max; Tian, Xiaochuan; Zhou, Zhi 78 2020 A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows. Zbl 1467.65098 Gunzburger, Max; Iliescu, Traian; Schneier, Michael 18 2020 An energy-based coupling approach to nonlocal interface problems. Zbl 1521.76117 Capodaglio, Giacomo; D’Elia, Marta; Bochev, Pavel; Gunzburger, Max 15 2020 Exponential time differencing for the tracer equations appearing in primitive equation ocean models. Zbl 1442.86001 Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D. 6 2020 Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional Laplace models. Zbl 1434.65224 Burkovska, Olena; Gunzburger, Max 6 2020 An optimally convergent higher-order finite element coupling method for interface and domain decomposition problems. Zbl 1453.65427 Cheung, James; Gunzburger, Max; Bochev, Pavel; Perego, Mauro 6 2020 High-precision computation of the weak Galerkin methods for the fourth-order problem. Zbl 1434.65238 Burkardt, John; Gunzburger, Max; Zhao, Wenju 5 2020 Auxiliary equations approach for the stochastic unsteady Navier-Stokes equations with additive random noise. Zbl 1463.65317 Zhao, Wenju; Gunzburger, Max 4 2020 Quantification of uncertainty: improving efficiency and technology. QUIET. Selected contributions based on the presentations at the international workshop, Trieste, Italy, July 18–21, 2017. Zbl 1454.62013 1 2020 Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs. Zbl 1455.62157 Capodaglio, Giacomo; Gunzburger, Max 1 2020 An efficient algorithm for simulating ensembles of parameterized flow problems. Zbl 1466.65133 Gunzburger, Max; Jiang, Nan; Wang, Zhu 30 2019 A second-order time-stepping scheme for simulating ensembles of parameterized flow problems. Zbl 1421.76157 Gunzburger, Max; Jiang, Nan; Wang, Zhu 22 2019 Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise. Zbl 1418.60077 Gunzburger, Max; Li, Buyang; Wang, Jilu 21 2019 Error analysis of fully discrete finite element approximations to an optimal control problem governed by a time-fractional PDE. Zbl 1417.65171 Gunzburger, Max; Wang, Jilu 18 2019 A localized reduced-order modeling approach for PDEs with bifurcating solutions. Zbl 1441.65082 Hess, Martin; Alla, Alessandro; Quaini, Annalisa; Rozza, Gianluigi; Gunzburger, Max 14 2019 Regularity analyses and approximation of nonlocal variational equality and inequality problems. Zbl 1421.49009 Burkovska, O.; Gunzburger, M. 14 2019 Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise. Zbl 1462.65143 Gunzburger, Max; Li, Buyang; Wang, Jilu 13 2019 Exponential time differencing for mimetic multilayer Ocean models. Zbl 1453.86019 Pieper, Konstantin; Sockwell, K. Chad; Gunzburger, Max 13 2019 Optimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries. Zbl 1417.65186 Cheung, James; Perego, Mauro; Bochev, Pavel; Gunzburger, Max 11 2019 A second-order Crank-Nicolson method for time-fractional PDEs. Zbl 1406.65060 Gunzburger, Max; Wang, Jilu 9 2019 An evolve-filter-relax stabilized reduced order stochastic collocation method for the time-dependent Navier-Stokes equations. Zbl 1428.65029 Gunzburger, M.; Iliescu, T.; Mohebujjaman, M.; Schneier, M. 7 2019 Descriptions, discretizations, and comparisons of time/space colored and white noise forcings of the Navier-Stokes equations. Zbl 1421.76156 Gunzburger, Max D.; Zhao, Wenju 5 2019 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 148 2018 On Stokes-Ritz projection and multistep backward differentiation schemes in decoupling the Stokes-Darcy model. Zbl 1465.65094 Gunzburger, Max; He, Xiaoming; Li, Buyang 33 2018 A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1402.35207 Gunzburger, Max; Jiang, Nan; Schneier, Michael 19 2018 Weak-Galerkin finite element methods for a second-order elliptic variational inequality. Zbl 1440.65204 Guan, Qingguang; Gunzburger, Max; Zhao, Wenju 17 2018 Convergence analysis of multifidelity Monte Carlo estimation. Zbl 1394.35492 Peherstorfer, Benjamin; Gunzburger, Max; Willcox, Karen 11 2018 Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion. Zbl 1409.76061 Gunzburger, Max; Jiang, Nan; Xu, Feifei 9 2018 Fast spherical centroidal Voronoi mesh generation: a Lloyd-preconditioned LBFGS method in parallel. Zbl 1415.65271 Yang, Huanhuan; Gunzburger, Max; Ju, Lili 1 2018 An ensemble-proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1394.76067 Gunzburger, Max; Jiang, Nan; Schneier, Michael 44 2017 Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes. Zbl 1436.35307 D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard 33 2017 Reduced basis methods for nonlocal diffusion problems with random input data. Zbl 1439.74415 Guan, Qingguang; Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan 10 2017 Analysis and approximation of a nonlocal obstacle problem. Zbl 1353.65064 Guan, Qingguang; Gunzburger, Max 8 2017 Comparison of approaches for random PDE optimization problems based on different matching functionals. Zbl 1370.49032 Lee, Hyung-Chun; Gunzburger, Max D. 8 2017 Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling. Zbl 1439.76136 Yang, Huanhuan; Gunzburger, Max 7 2017 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009 Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 51 2016 An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system. Zbl 1388.76127 Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 31 2016 Identification of the diffusion parameter in nonlocal steady diffusion problems. Zbl 1342.49053 D’Elia, M.; Gunzburger, M. 27 2016 Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Zbl 1356.65239 Tian, Xiaochuan; Du, Qiang; Gunzburger, Max 17 2016 A two phase field model for tracking vesicle-vesicle adhesion. Zbl 1366.92019 Gu, Rui; Wang, Xiaoqiang; Gunzburger, Max 12 2016 A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions. Zbl 1436.74076 Xu, Feifei; Gunzburger, Max; Burkardt, John 11 2016 Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection. Zbl 1386.65083 Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; Burkardt, John 9 2016 Quadrature rules for finite element approximations of 1D nonlocal problems. Zbl 1349.65729 Zhang, Xiaoping; Gunzburger, Max; Ju, Lili 9 2016 A multiscale implementation based on adaptive mesh refinement for the nonlocal peridynamics model in one dimension. Zbl 1381.74214 Xu, Feifei; Gunzburger, Max; Burkardt, John; Du, Qiang 8 2016 Nodal-type collocation methods for hypersingular integral equations and nonlocal diffusion problems. Zbl 1425.65215 Zhang, Xiaoping; Gunzburger, Max; Ju, Lili 6 2016 Numerical methods for a class of nonlocal diffusion problems with the use of backward SDEs. Zbl 1443.65266 Zhang, Guannan; Zhao, Weidong; Webster, Clayton; Gunzburger, Max 3 2016 A least-squares finite element method for a nonlinear Stokes problem in glaciology. Zbl 1443.65360 Monnesland, Irene Sonja; Lee, Eunjung; Gunzburger, Max; Yoon, Ryeongkyung 1 2016 Stochastic steady-state Navier-Stokes equations with additive random noise. Zbl 06555593 Gunzburger, Max D.; Hou, Lisheng; Ming, Ju 1 2016 Fractional diffusion on bounded domains. Zbl 1488.35557 Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M. 59 2015 A multilevel stochastic collocation method for partial differential equations with random input data. Zbl 1327.65014 Teckentrup, A. L.; Jantsch, P.; Webster, C. G.; Gunzburger, M. 56 2015 Peridynamics and material interfaces. Zbl 1455.74009 Alali, Bacim; Gunzburger, Max 25 2015 \(\theta\) schemes for finite element discretization of the space-time fractional diffusion equations. Zbl 1320.65141 Guan, Qingguang; Gunzburger, Max 13 2015 Stability and accuracy of time-stepping schemes and dispersion relations for a nonlocal wave equation. Zbl 1309.65106 Guan, Qingguang; Gunzburger, Max 9 2015 A generalized nonlocal vector calculus. Zbl 1331.26018 Alali, Bacim; Liu, Kuo; Gunzburger, Max 8 2015 Stability and convergence of time-stepping methods for a nonlocal model for diffusion. Zbl 1334.65145 Guan, Qingguang; Gunzburger, Max 6 2015 Power-law noises over general spatial domains and on nonstandard meshes. Zbl 1322.65024 van Wyk, Hans-Werner; Gunzburger, Max; Burkhardt, John; Stoyanov, Miroslav 4 2015 A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection. Zbl 1317.65058 Zhang, G.; Webster, C.; Gunzburger, M.; Burkardt, J. 2 2015 Stochastic finite element methods for partial differential equations with random input data. Zbl 1398.65299 Gunzburger, Max D.; Webster, Clayton G.; Zhang, Guannan 106 2014 Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems. Zbl 1457.65089 Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 101 2014 Optimal distributed control of nonlocal steady diffusion problems. Zbl 1298.49006 D’Elia, Marta; Gunzburger, Max 26 2014 An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data. Zbl 1316.65011 Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan 18 2014 Peridynamic state-based models and the embedded-atom model. Zbl 1373.82029 Seleson, Pablo; Parks, Michael L.; Gunzburger, Max 17 2014 Simulating vesicle-substrate adhesion using two phase field functions. Zbl 1349.92050 Gu, R.; Wang, X.; Gunzburger, M. 10 2014 An efficient and accurate method for the identification of the most influential random parameters appearing in the input data for PDEs. Zbl 1426.76634 Labovsky, A.; Gunzburger, Max 4 2014 An adaptive sparse-grid iterative ensemble Kalman filter approach for parameter field estimation. Zbl 1383.76393 Webster, Clayton G.; Zhang, Guannan; Gunzburger, Max 4 2014 Goal-oriented a posteriori error estimation for finite volume methods. Zbl 1293.65116 Chen, Qingshan; Gunzburger, Max 3 2014 Finite element three-dimensional Stokes ice sheet dynamics model with enhanced local mass conservation. Zbl 1351.86030 Leng, Wei; Ju, Lili; Xie, Yan; Cui, Tao; Gunzburger, Max 2 2014 A parallel computational model for three-dimensional, thermo-mechanical Stokes flow simulations of glaciers and ice sheets. Zbl 1373.86004 Leng, Wei; Ju, Lili; Gunzburger, Max; Price, Stephen 2 2014 Editorial: Minimum residual and least squares finite element methods. Zbl 1365.00053 1 2014 A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 221 2013 The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. Zbl 1345.35128 D’Elia, Marta; Gunzburger, Max 121 2013 Efficient and long-time accurate second-order methods for the Stokes-Darcy system. Zbl 1282.76094 Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 68 2013 Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Zbl 1286.74010 Seleson, Pablo; Gunzburger, Max; Parks, Michael L. 45 2013 Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 40 2013 A sparse-grid method for multi-dimensional backward stochastic differential equations. Zbl 1289.65011 Zhang, Guannan; Gunzburger, Max; Zhao, Weidong 25 2013 A co-volume scheme for the rotating shallow water equations on conforming non-orthogonal grids. Zbl 1426.76346 Chen, Qingshan; Ringler, Todd; Gunzburger, Max 11 2013 A distributed control approach for the boundary optimal control of the steady MHD equations. Zbl 1373.76339 Bornia, G.; Gunzburger, M.; Manservisi, S. 7 2013 Well-posedness results for a nonlinear Stokes problem arising in glaciology. Zbl 1282.35292 Chen, Qingshan; Gunzburger, Max; Perego, Mauro 6 2013 Coarse-grid sampling interpolatory methods for approximating Gaussian random fields. Zbl 1401.60094 D’Elia, Marta; Gunzburger, Max 5 2013 Unified matching grids for multidomain multiphysics simulations. Zbl 1285.65081 Womeldorff, G.; Peterson, J.; Gunzburger, M.; Ringler, T. 2 2013 Efficient numerical methods for stochastic partial differential equations through transformation to equations driven by correlated noise. Zbl 1515.65029 Ming, Ju; Gunzburger, Max 2 2013 Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168 Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 327 2012 Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data. Zbl 1260.65007 Zhang, Guannan; Gunzburger, Max 22 2012 High accuracy method for turbulent flow problems. Zbl 1437.76039 Gunzburger, M.; Labovsky, A. 16 2012 A finite element, filtered eddy-viscosity method for the Navier-Stokes equations with large Reynolds number. Zbl 1254.76100 Lee, Eunjung; Gunzburger, Max D. 1 2012 A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. Zbl 1414.76017 Chen, Wenbin; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 96 2011 Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Zbl 1225.74082 Chen, X.; Gunzburger, Max 94 2011 Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Zbl 1305.76072 Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 90 2011 Error estimates of stochastic optimal Neumann boundary control problems. Zbl 1243.65008 Gunzburger, Max D.; Lee, Hyung-Chun; Lee, Jangwoon 37 2011 ...and 192 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 5,988 Authors 144 Gunzburger, Max D. 97 Du, Qiang 57 He, Yinnian 54 Li, Jian 51 Rozza, Gianluigi 50 Ju, Lili 36 D’Elia, Marta 35 Bochev, Pavel B. 34 Huang, Pengzhan 33 Hou, Yanren 31 Feng, Xinlong 30 Chen, Zhangxin 30 He, Xiaoming 30 Layton, William J. 29 Zheng, Haibiao 28 Tian, Xiaochuan 27 Luo, Zhendong 26 Wang, Zhu 25 Protas, Bartosz 24 Iliescu, Traian 23 Wang, Hong 23 Yang, Suh-Yuh 22 Zhang, Tong 21 Chen, Yanping 20 Huang, Yunqing 20 Lee, Hyesuk Kwon 20 Peherstorfer, Benjamin 19 Gerritsma, Marc I. 19 Jiang, Nan 19 Lee, Hyung-Chun 19 Rebholz, Leo G. 19 Si, Zhiyong 19 Takahashi, Takéo 18 Navon, Ionel Michael 18 Su, Haiyan 18 Wang, Xiaoming 17 Du, Guangzhi 17 Manzoni, Andrea 17 Pan, Xingbin 17 Shang, Yueqiang 17 Yang, Xiaofeng 17 Zhang, Guodong 16 Mei, Liquan 16 Webster, Clayton G. 15 Ballarin, Francesco 15 Chen, Wenbin 15 Muha, Boris 15 Otárola, Enrique 15 Rossi, Julio Daniel 15 Zhang, Guannan 15 Zuo, Liyun 14 Antoine, Xavier 14 Codina, Ramon 14 Feng, Minfu 14 Lee, Eunjung 14 Quarteroni, Alfio M. 14 Shadid, John N. 14 Trenchea, Catalin 14 Zhang, Jiwei 13 Al Mahbub, Md. Abdullah 13 Alekseev, Gennady V. 13 Chrysafinos, Konstantinos 13 Khan, Akhtar Ali 13 Kunisch, Karl 13 Labovsky, Alexander E. 13 Li, Rui 13 Manservisi, Sandro 13 Mengesha, Tadele 13 Nie, Yufeng 13 Peterson, Janet S. 13 Qin, Yi 13 Ravindran, Sivaguru S. 13 Turkel, Eli L. 13 Warma, Mahamadi 13 Willcox, Karen E. 13 Yang, Huanhuan 13 Yu, Yue 12 An, Rong 12 Cao, Yanzhao 12 Dassi, Franco 12 Deng, Weihua 12 Ghattas, Omar N. 12 Hesthaven, Jan S. 12 Karniadakis, George Em 12 Lehoucq, Richard B. 12 Li, Buyang 12 Li, Yuan 12 Lu, Zuliang 12 Schröder, Jörg 12 Shi, Dongyang 12 Shi, Feng 12 Singler, John R. 12 Yan, Wenjing 12 Zheng, Xiangcheng 11 Bellido, José Carlos 11 Burkardt, John V. 11 Čanić, Sunčica 11 Duan, Huoyuan 11 Ervin, Vincent J. 11 Foster, John T. jun. ...and 5,888 more Authors all top 5 Cited in 416 Serials 464 Computer Methods in Applied Mechanics and Engineering 353 Journal of Computational Physics 265 Computers & Mathematics with Applications 180 Journal of Scientific Computing 169 Journal of Computational and Applied Mathematics 136 Applied Mathematics and Computation 121 Applied Numerical Mathematics 112 SIAM Journal on Scientific Computing 108 Numerical Methods for Partial Differential Equations 99 SIAM Journal on Numerical Analysis 82 Journal of Mathematical Analysis and Applications 79 International Journal for Numerical Methods in Engineering 73 Numerische Mathematik 64 Computers and Fluids 59 Mathematics of Computation 58 Computational Mechanics 58 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 51 SIAM/ASA Journal on Uncertainty Quantification 50 Advances in Computational Mathematics 46 International Journal for Numerical Methods in Fluids 46 Numerical Algorithms 41 Journal of Fluid Mechanics 38 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 38 Numerical Functional Analysis and Optimization 37 Mathematical Methods in the Applied Sciences 34 Applied Mathematical Modelling 34 Communications in Computational Physics 33 Journal of Differential Equations 32 International Journal of Computer Mathematics 32 International Journal of Numerical Analysis and Modeling 30 Advances in Applied Mathematics and Mechanics 29 Applied Mathematics Letters 27 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 25 Applicable Analysis 25 Mathematics and Computers in Simulation 25 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 23 Archive for Rational Mechanics and Analysis 23 Communications in Nonlinear Science and Numerical Simulation 22 Applied Mathematics and Optimization 22 Physica D 22 SIAM Journal on Mathematical Analysis 22 International Journal of Computational Fluid Dynamics 22 Discrete and Continuous Dynamical Systems. Series B 22 Computational Methods in Applied Mathematics 21 Computational Geosciences 20 Multiscale Modeling & Simulation 19 SIAM Journal on Control and Optimization 19 Calculus of Variations and Partial Differential Equations 19 Engineering Analysis with Boundary Elements 18 ZAMP. Zeitschrift für angewandte Mathematik und Physik 17 Inverse Problems 17 Journal of Mathematical Physics 17 Evolution Equations and Control Theory 17 East Asian Journal on Applied Mathematics 16 Journal of Mathematical Fluid Mechanics 15 BIT 15 Acta Applicandae Mathematicae 15 Computational and Applied Mathematics 15 Science China. Mathematics 14 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 14 Journal of Elasticity 14 Mathematical Problems in Engineering 13 Computer Physics Communications 13 Communications in Numerical Methods in Engineering 13 Physics of Fluids 13 Journal of Numerical Mathematics 12 Wave Motion 12 Calcolo 12 Applied Mathematics and Mechanics. (English Edition) 12 Discrete and Continuous Dynamical Systems 12 Abstract and Applied Analysis 11 Transactions of the American Mathematical Society 11 Applications of Mathematics 11 Computational Optimization and Applications 11 Fractional Calculus & Applied Analysis 11 European Journal of Mechanics. B. Fluids 11 Numerical Mathematics: Theory, Methods and Applications 10 Computer Aided Geometric Design 10 RAIRO. Modélisation Mathématique et Analyse Numérique 10 Optimization and Engineering 10 Archives of Computational Methods in Engineering 10 SIAM Journal on Imaging Sciences 9 International Journal of Control 9 Journal of Optimization Theory and Applications 9 Japan Journal of Industrial and Applied Mathematics 9 International Journal of Computational Methods 9 Advances in Difference Equations 9 Discrete and Continuous Dynamical Systems. Series S 8 Communications in Mathematical Physics 8 Journal of Engineering Mathematics 8 Journal of the Mechanics and Physics of Solids 8 Journal of Functional Analysis 8 Chinese Annals of Mathematics. Series B 8 SIAM Review 8 Journal of Nonlinear Science 8 Mathematics and Mechanics of Solids 8 Journal of Dynamical and Control Systems 8 Acta Numerica 8 Mathematical Control and Related Fields 8 Nonlinear Analysis. Theory, Methods & Applications ...and 316 more Serials all top 5 Cited in 51 Fields 2,958 Numerical analysis (65-XX) 2,065 Fluid mechanics (76-XX) 2,045 Partial differential equations (35-XX) 686 Mechanics of deformable solids (74-XX) 578 Calculus of variations and optimal control; optimization (49-XX) 244 Probability theory and stochastic processes (60-XX) 214 Statistical mechanics, structure of matter (82-XX) 188 Systems theory; control (93-XX) 148 Computer science (68-XX) 141 Statistics (62-XX) 126 Integral equations (45-XX) 120 Biology and other natural sciences (92-XX) 118 Optics, electromagnetic theory (78-XX) 110 Operations research, mathematical programming (90-XX) 99 Operator theory (47-XX) 94 Real functions (26-XX) 91 Geophysics (86-XX) 76 Classical thermodynamics, heat transfer (80-XX) 70 Approximations and expansions (41-XX) 57 Ordinary differential equations (34-XX) 53 Functional analysis (46-XX) 39 Linear and multilinear algebra; matrix theory (15-XX) 36 Information and communication theory, circuits (94-XX) 34 Dynamical systems and ergodic theory (37-XX) 33 Global analysis, analysis on manifolds (58-XX) 31 Quantum theory (81-XX) 30 Mechanics of particles and systems (70-XX) 26 Harmonic analysis on Euclidean spaces (42-XX) 20 Convex and discrete geometry (52-XX) 18 Combinatorics (05-XX) 17 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Measure and integration (28-XX) 14 Special functions (33-XX) 13 General and overarching topics; collections (00-XX) 11 Potential theory (31-XX) 10 Differential geometry (53-XX) 7 Integral transforms, operational calculus (44-XX) 7 Astronomy and astrophysics (85-XX) 6 Difference and functional equations (39-XX) 3 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Group theory and generalizations (20-XX) 2 Geometry (51-XX) 1 Number theory (11-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.