Edit Profile (opens in new tab) Gunzburger, Max D. Compute Distance To: Compute 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: 311 Publications since 1970, including 3 Books 10 Contributions as Editor Biographic References: 3 Publications Co-Authors: 165 Co-Authors with 303 Joint Publications 3,858 Co-Co-Authors all top 5 Co-Authors 15 single-authored 36 Du, Qiang 29 Peterson, Janet S. 28 Bochev, Pavel B. 22 Ju, Lili 16 Nicolaides, Roy A. 15 Burkardt, John V. 12 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 D’Elia, Marta 9 Fix, George J. 8 Svobodny, Thomas P. 7 Fursikov, Andreĭ Vladimirovich 7 Parks, Michael L. 6 Guan, Qingguang 6 Wang, Zhu 5 Hou, Lisheng 5 Jiang, Nan 5 Lee, Eunjung 5 Schneier, Michael 5 Trenchea, Catalin 5 Wang, Jilu 4 Badia, Santiago 4 Chapman, Stephen Jonathan 4 Chen, Qingshan 4 Chen, Wenbin 4 Hua, Fei 4 Li, Buyang 4 Saka, Yuki 4 Seleson, Pablo 4 Shadid, John N. 4 Willcox, Karen E. 4 Wood, Houston G. III 4 Zhao, Weidong 4 Zhao, Wenju 3 Burkhardt, John 3 Burkovska, Olena 3 Capodaglio, Giacomo 3 Cliff, Eugene M. 3 Deang, Jennifer M. 3 He, Xiaoming 3 Kim, Hongchul 3 Kunoth, Angela 3 Lee, Hyesuk Kwon 3 Lee, Jeehyun 3 Leng, Wei 3 Liu, Chen-Huei 3 Peherstorfer, Benjamin 3 Perego, Mauro 3 Ringler, Todd D. 3 Turner, James C. jun. 3 Wang, Xiaoqiang 3 Xu, Feifei 3 Zhang, Yanzhi 3 Zhou, Kun 3 Zhu, Wenxiang 2 Alali, Bacim 2 Burns, John A. 2 Calhoun-Lopez, Marcus 2 Chang, Ching Lung 2 Chen, Zheng 2 Cheung, James 2 Choi, Jungmin 2 Gottlieb, David I. 2 Gruber, Anthony 2 Gu, Rui 2 Iliescu, Traian 2 Jordan, Jo Ann 2 Lan, Rihui 2 Layton, William J. 2 Ming, Ju 2 Pieper, Konstantin 2 Rozza, Gianluigi 2 Sun, Dong 2 Ting, Lu 2 Turkel, Eli L. 2 Yang, Huanhuan 2 Yang, Sung-Dae 2 Zhang, Xiaoping 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 1 Castaño Díez, Daniel 1 Chen, Nan 1 Chen, Puying 1 Chen, Xi 1 Chrysafinos, Konstantinos 1 Cox, Christopher L. 1 Cui, Tao ...and 65 more Co-Authors all top 5 Serials 25 Computer Methods in Applied Mechanics and Engineering 24 SIAM Journal on Numerical Analysis 21 Computers & Mathematics with Applications 11 Journal of Computational Physics 10 SIAM Journal on Control and Optimization 9 Journal of Mathematical Analysis and Applications 9 Numerische Mathematik 9 SIAM Journal on Scientific Computing 8 Mathematics of Computation 6 SIAM Review 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Applied Mathematics and Computation 5 Multiscale Modeling & Simulation 5 International Journal of Numerical Analysis and Modeling 5 Communications in Computational Physics 5 Numerical Mathematics: Theory, Methods and Applications 5 SIAM/ASA Journal on Uncertainty Quantification 4 Computers and Fluids 4 Journal of Computational and Applied Mathematics 4 Applied Mathematics Letters 4 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 AIAA Journal 3 International Journal for Numerical Methods in Fluids 3 Numerical Methods for Partial Differential Equations 3 Journal of Scientific Computing 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 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 Oberwolfach Reports 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 Applied Mathematics and Optimization 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 Acta Numerica 1 Applied Mathematical Sciences 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Computational Science and Engineering 1 Advances in Design and Control 1 International Journal for Uncertainty Quantification 1 Results in Applied Mathematics all top 5 Fields 195 Numerical analysis (65-XX) 157 Fluid mechanics (76-XX) 135 Partial differential equations (35-XX) 58 Calculus of variations and optimal control; optimization (49-XX) 24 Mechanics of deformable solids (74-XX) 22 Probability theory and stochastic processes (60-XX) 19 Statistical mechanics, structure of matter (82-XX) 18 Systems theory; control (93-XX) 11 General and overarching topics; collections (00-XX) 10 Statistics (62-XX) 10 Geophysics (86-XX) 9 Integral equations (45-XX) 8 Mechanics of particles and systems (70-XX) 5 Real functions (26-XX) 5 Computer science (68-XX) 5 Optics, electromagnetic theory (78-XX) 5 Biology and other natural sciences (92-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Functional analysis (46-XX) 3 Convex and discrete geometry (52-XX) 3 Classical thermodynamics, heat transfer (80-XX) 3 Operations research, mathematical programming (90-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Ordinary differential equations (34-XX) 2 Information and communication theory, circuits (94-XX) 1 Combinatorics (05-XX) 1 Potential theory (31-XX) 1 Special functions (33-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 276 Publications have been cited 6,208 times in 3,898 Documents Cited by ▼ Year ▼ Centroidal Voronoi tessellations: Applications and algorithms. Zbl 0983.65021Du, Qiang; Faber, Vance; Gunzburger, Max 241 1999 Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 239 2012 Stabilization of low-order mixed finite elements for the Stokes equations. Zbl 1145.76015Bochev, Pavel B.; Dohrmann, Clark R.; Gunzburger, Max D. 212 2006 Perspectives in flow control and optimization. Zbl 1088.93001Gunzburger, Max D. 187 2003 A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Zbl 1266.26020Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 168 2013 Boundary conditions for the numerical solution of elliptic equations in exterior regions. Zbl 0479.65056Bayliss, Alvin; Gunzburger, Max; Turkel, Eli 159 1982 Finite element methods for viscous incompressible flows. Zbl 0697.76031Gunzburger, Max D. 156 1989 Least-squares finite element methods. Zbl 1168.65067Bochev, Pavel B.; Gunzburger, Max D. 146 2009 On the existence, uniqueness, and finite element approximation of solutions of the equations of stationary, incompressible magnetohydrodynamics. Zbl 0731.76094Gunzburger, Max D.; Meir, Amnon J.; Peterson, Janet S. 145 1991 Analysis and approximation of the Ginzburg-Landau model of superconductivity. Zbl 0787.65091Du, Qiang; Gunzburger, Max D.; Peterson, Janet S. 138 1992 Finite element methods of least-squares type. Zbl 0914.65108Bochev, Pavel B.; Gunzburger, Max D. 117 1998 Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. Zbl 1189.35244Cao, Yanzhao; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 109 2010 Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. Zbl 1252.76040Cao, Yanzhao; Gunzburger, Max; Hu, Xiaolong; Hua, Fei; Wang, Xiaoming; Zhao, Weidong 106 2010 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 98 2018 The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. Zbl 1345.35128D’Elia, Marta; Gunzburger, Max 91 2013 Stochastic finite element methods for partial differential equations with random input data. Zbl 1398.65299Gunzburger, Max D.; Webster, Clayton G.; Zhang, Guannan 80 2014 POD and CVT-based reduced-order modeling of Navier-Stokes flows. Zbl 1120.76323Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun 79 2006 A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. Zbl 1414.76017Chen, Wenbin; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 79 2011 Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems. Zbl 1457.65089Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 78 2014 Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Zbl 1305.76072Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 73 2011 Analysis of a linear fluid-structure interaction problem. Zbl 1039.35076Du, Qiang; Gunzburger, M. D.; Hou, L. S.; Lee, J. 70 2003 Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Zbl 1225.74082Chen, X.; Gunzburger, Max 69 2011 A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057Gunzburger, Max; Lehoucq, R. B. 67 2010 Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. Zbl 0970.35096Gunzburger, Max D.; Lee, Hyung-Chun; Seregin, Gregory A. 65 2000 Boundary velocity control of incompressible flow with an application to viscous drag reduction. Zbl 0756.49004Gunzburger, Max D.; Hou, Lisheng; Svobodny, Thomas P. 64 1992 Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. Zbl 0963.35150Gunzburger, M. D.; Manservisi, S. 59 2000 Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data. Zbl 1121.65354Gunzburger, Max D.; Peterson, Janet S.; Shadid, John N. 57 2007 Analysis of least squares finite element methods for the Stokes equations. Zbl 0816.65082Bochev, Pavel B.; Gunzburger, Max D. 56 1994 Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. Zbl 0737.76045Gunzburger, M. D.; Hou, L. S.; Svobodny, Th. P. 56 1991 Finite-dimensional approximation of a class of constrained nonlinear optimal control problems. Zbl 0849.49005Gunzburger, Max D.; Hou, L. Steven 55 1996 Efficient and long-time accurate second-order methods for the Stokes-Darcy system. Zbl 1282.76094Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 51 2013 A taxonomy of consistently stabilized finite element methods for the Stokes problem. Zbl 1133.76307Barth, Teri; Bochev, Pavel; Gunzburger, Max; Shadid, John 49 2004 Fractional diffusion on bounded domains. Zbl 1488.35557Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M. 48 2015 Issues related to least-squares finite element methods for the Stokes equations. Zbl 0953.65083Deang, Jennifer M.; Gunzburger, Max D. 48 1999 Constrained centroidal Voronoi tessellations for surfaces. Zbl 1036.65101Du, Qiang; Gunzburger, Max D.; Ju, Lili 46 2003 The velocity tracking problem for Navier-Stokes flows with bounded distributed controls. Zbl 0938.35118Gunzburger, M. D.; Manservisi, S. 45 1999 Least-squares methods for the velocity-pressure-stress formulation of the Stokes equations. Zbl 1067.76562Bochev, Pavel B.; Gunzburger, Max D. 45 1995 A multilevel stochastic collocation method for partial differential equations with random input data. Zbl 1327.65014Teckentrup, A. L.; Jantsch, P.; Webster, C. G.; Gunzburger, M. 44 2015 Peridynamics as an upscaling of molecular dynamics. Zbl 1375.82073Seleson, Pablo; Parks, Michael L.; Gunzburger, Max; Lehoucq, Richard B. 43 2009 Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Zbl 1173.74303Fish, Jacob; Nuggehally, Mohan A.; Shephard, Mark S.; Picu, Catalin R.; Badia, Santiago; Parks, Michael L.; Gunzburger, Max 41 2007 Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls. Zbl 0747.76063Gunzburger, M. D.; Hou, L.; Svobodny, T. P. 41 1991 The velocity tracking problem for Navier-Stokes flows with boundary control. Zbl 0991.49002Gunzburger, M. D.; Manservisi, S. 40 2000 Self-contained automated methodology for optimal flow control. Zbl 0901.76067Joslin, Ronald D.; Gunzburger, Max D.; Nicolaides, Roy A.; Erlebacher, Gordon; Hussaini, M. Yousuff 39 1997 Analysis of a Ladyzhenskaya model for incompressible viscous flow. Zbl 0712.76039Du, Qiang; Gunzburger, Max D. 39 1991 Grid generation and optimization based on centroidal Voronoi tessellations. Zbl 1024.65118Du, Qiang; Gunzburger, Max 37 2002 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 36 2016 Boundary value problems and optimal boundary control for the Navier-Stokes system: The two-dimensional case. Zbl 0910.76011Fursikov, A. V.; Gunzburger, M. D.; Hou, L. S. 36 1998 An absolutely stable pressure-Poisson stabilized finite element method for the Stokes equations. Zbl 1159.76346Bochev, Pavel; Gunzburger, Max 36 2004 Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system. Zbl 1352.35093Chen, Nan; Gunzburger, Max; Wang, Xiaoming 35 2010 On atomistic-to-continuum coupling by blending. Zbl 1160.65338Badia, Santiago; Parks, Michael; Bochev, Pavel; Gunzburger, Max; Lehoucq, Richard 35 2008 Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 34 2013 On the global unique solvability of initial-boundary value problems for the coupled modified Navier-Stokes and Maxwell equations. Zbl 1064.76118Gunzburger, M. D.; Ladyzhenskaya, O. A.; Peterson, J. S. 31 2004 On finite element methods of the least squares type. Zbl 0422.65064Fix, George J.; Gunzburger, Max D.; Nicolaides, R. A. 31 1979 Accuracy of least-squares methods for the Navier–Stokes equations. Zbl 0779.76039Bochev, Pavel B.; Gunzburger, Max D. 30 1993 Sensitivities, adjoints and flow optimization. Zbl 0962.76030Gunzburger, Max D. 30 1999 On stabilized finite element methods for the Stokes problem in the small time step limit. Zbl 1104.76059Bochev, Pavel B.; Gunzburger, Max D.; Lehoucq, Richard B. 30 2007 Error estimates of stochastic optimal Neumann boundary control problems. Zbl 1243.65008Gunzburger, Max D.; Lee, Hyung-Chun; Lee, Jangwoon 30 2011 Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Zbl 1286.74010Seleson, Pablo; Gunzburger, Max; Parks, Michael L. 30 2013 On mixed finite element methods for first order elliptic systems. Zbl 0459.65072Fix, G. J.; Gunzburger, M. D.; Nicolaides, R. A. 29 1981 Stability of the SUPG finite element method for transient advection-diffusion problems. Zbl 1067.76563Bochev, Pavel B.; Gunzburger, Max D.; Shadid, John N. 28 2004 An ensemble-proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1394.76067Gunzburger, Max; Jiang, Nan; Schneier, Michael 28 2017 Optimal boundary control for the evolutionary Navier-Stokes system: The three-dimensional case. Zbl 1076.76029Fursikov, A. V.; Gunzburger, M. D.; Hou, L. S. 27 2005 Adjoint equation-based methods for control problems in incompressible, viscous flows. Zbl 0996.76024Gunzburger, Max 26 2000 An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system. Zbl 1388.76127Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 24 2016 On Stokes-Ritz projection and multistep backward differentiation schemes in decoupling the Stokes-Darcy model. Zbl 1465.65094Gunzburger, Max; He, Xiaoming; Li, Buyang 24 2018 Probabilistic methods for centroidal Voronoi tessellations and their parallel implementations. Zbl 1014.68202Ju, Lili; Du, Qiang; Gunzburger, Max 24 2002 A Ginzburg-Landau type model of superconducting normal junctions including Josephson junctions. Zbl 0843.35120Chapman, S. Jonathan; Du, Qiang; Gunzburger, Max D. 24 1995 An optimization-based domain decomposition method for the Navier-Stokes equations. Zbl 1003.76024Gunzburger, Max D.; Lee, Hyesuk Kwon 24 2000 Finite-element approximations of a Ladyzhenskaya model for stationary incompressible viscous flow. Zbl 0697.76046Du, Qiang; Gunzburger, Max D. 24 1990 Centroidal Voronoi tessellation-based reduced-order modeling of complex systems. Zbl 1111.65084Burkardt, John; Gunzburger, Max; Lee, Hyung-Chun 23 2006 An optimization based domain decomposition method for partial differential equations. Zbl 0941.65123Gunzburger, M. D.; Peterson, J. S.; Kwon, H. 23 1999 Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere. Zbl 1046.65094Du, Qiang; Gunzburger, Max D.; Ju, Lili 21 2003 A finite element method for first order elliptic systems in three dimensions. Zbl 0631.65108Chang, Ching-Lung; Gunzburger, Max D. 21 1987 Superconvergence analysis of FEMs for the Stokes-Darcy system. Zbl 1303.76086Chen, Wenbin; Chen, Puying; Gunzburger, Max; Yan, Ningning 21 2010 On inf–sup stabilized finite element methods for transient problems. Zbl 1079.76577Bochev, Pavel B.; Gunzburger, Max D.; Shadid, John N. 21 2004 Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032Du, Qiang; Gunzburger, Max; Ju, Lili 21 2010 A locally conservative least-squares method for Darcy flows. Zbl 1191.76066Bochev, P. B.; Gunzburger, M. D. 21 2008 A model for variable thickness superconducting thin films. Zbl 0862.35119Chapman, S. J.; Du, Qiang; Gunzburger, M. D. 20 1996 On least squares approximations to indefinite problems of the mixed type. Zbl 0378.76046Fix, George J.; Gunzburger, Max D. 20 1978 Adaptive finite element methods for elliptic PDEs based on conforming centroidal Voronoi-Delaunay triangulations. Zbl 1126.65099Ju, Lili; Gunzburger, Max; Zhao, Weidong 20 2006 On least-squares finite element methods for the Poisson equation and their connection to the Dirichlet and Kelvin principles. Zbl 1128.76031Bochev, Pavel; Gunzburger, Max 19 2005 On conforming finite element methods for the inhomogeneous stationary Navier-Stokes equations. Zbl 0559.76026Gunzburger, Max D.; Peterson, Janet S. 19 1983 On numerical boundary treatment of hyperbolic systems for finite difference and finite element methods. Zbl 0481.65072Gottlieb, David; Gunzburger, Max; Turkel, Eli 19 1982 A sparse-grid method for multi-dimensional backward stochastic differential equations. Zbl 1289.65011Zhang, Guannan; Gunzburger, Max; Zhao, Weidong 19 2013 Least-squares finite element methods. Zbl 1100.65098Bochev, Pavel; Gunzburger, Max 18 2006 Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations. Zbl 0917.49004Gunzburger, Max D.; Kim, Hongchul 18 1998 Least-squares finite element approximations to solutions of interface problems. Zbl 0913.65096Cao, Yanzhao; Gunzburger, Max D. 18 1998 An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data. Zbl 1316.65011Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan 18 2014 Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses. Zbl 0748.76073Gunzburger, Max D.; Hou, Steven L. 17 1992 Feedback control of Karman vortex shedding. Zbl 0875.76073Gunzburger, M. D.; Lee, H. C. 17 1996 Meshfree, probabilistic determination of point sets and support regions for meshless computing. Zbl 0993.65009Du, Qiang; Gunzburger, Max; Ju, Lili 15 2002 Analysis and discretization of an optimal control problem for the time-periodic MHD equations. Zbl 1073.49003Gunzburger, Max; Trenchea, Catalin 15 2005 Incompressible computational fluid dynamics: trends and advances. Zbl 1190.76004 15 1993 Semidiscrete finite element approximations of a linear fluid-structure interaction problem. Zbl 1159.74343Du, Qiang; Gunzburger, M. D.; Hou, Lisheng; Lee, Jeehyun 15 2004 Identification of the diffusion parameter in nonlocal steady diffusion problems. Zbl 1342.49053D’Elia, M.; Gunzburger, M. 15 2016 ANOVA expansions and efficient sampling methods for parameter dependent nonlinear PDEs. Zbl 1161.65336Cao, Yanzhao; Chen, Zheng; Gunzburger, Max 15 2009 Optimal distributed control of nonlocal steady diffusion problems. Zbl 1298.49006D’Elia, Marta; Gunzburger, Max 15 2014 On finite element approximations of problems having inhomogeneous essential boundary conditions. Zbl 0531.65056Fix, George J.; Gunzburger, Max D.; Peterson, Janet S. 15 1983 Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data. Zbl 1260.65007Zhang, Guannan; Gunzburger, Max 15 2012 A subdomain-Galerkin/least squares method for first-order elliptic systems in the plane. Zbl 0717.65087Chang, Ching-Lung; Gunzburger, Max D. 15 1990 A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems. Zbl 1473.65188D’Elia, Marta; Gunzburger, Max; Vollmann, Christian 3 2021 Approximation of probability density functions for PDEs with random parameters using truncated series expansions. Zbl 1471.62309Capodaglio, Giacomo; Gunzburger, Max; Wynn, Henry P. 1 2021 Parallel exponential time differencing methods for geophysical flow simulations. Zbl 07427389Lan, Rihui; Leng, Wei; Wang, Zhu; Ju, Lili; Gunzburger, Max 1 2021 On a nonlocal Cahn-Hilliard model permitting sharp interfaces. Zbl 1484.35352Burkovska, Olena; Gunzburger, Max 1 2021 An energy-based coupling approach to nonlocal interface problems. Zbl 07211869Capodaglio, Giacomo; D’Elia, Marta; Bochev, Pavel; Gunzburger, Max 8 2020 A Leray regularized ensemble-proper orthogonal decomposition method for parameterized convection-dominated flows. Zbl 1467.65098Gunzburger, Max; Iliescu, Traian; Schneier, Michael 6 2020 Exponential time differencing for the tracer equations appearing in primitive equation ocean models. Zbl 1442.86001Calandrini, Sara; Pieper, Konstantin; Gunzburger, Max D. 5 2020 Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional Laplace models. Zbl 1434.65224Burkovska, Olena; Gunzburger, Max 3 2020 An optimally convergent higher-order finite element coupling method for interface and domain decomposition problems. Zbl 1453.65427Cheung, James; Gunzburger, Max; Bochev, Pavel; Perego, Mauro 3 2020 High-precision computation of the weak Galerkin methods for the fourth-order problem. Zbl 1434.65238Burkardt, John; Gunzburger, Max; Zhao, Wenju 2 2020 Auxiliary equations approach for the stochastic unsteady Navier-Stokes equations with additive random noise. Zbl 1463.65317Zhao, Wenju; Gunzburger, Max 2 2020 Piecewise polynomial approximation of probability density functions with application to uncertainty quantification for stochastic PDEs. Zbl 1455.62157Capodaglio, Giacomo; Gunzburger, Max 1 2020 Sharp convergence rates of time discretization for stochastic time-fractional PDEs subject to additive space-time white noise. Zbl 1418.60077Gunzburger, Max; Li, Buyang; Wang, Jilu 14 2019 A second-order time-stepping scheme for simulating ensembles of parameterized flow problems. Zbl 1421.76157Gunzburger, Max; Jiang, Nan; Wang, Zhu 12 2019 Regularity analyses and approximation of nonlocal variational equality and inequality problems. Zbl 1421.49009Burkovska, O.; Gunzburger, M. 8 2019 A second-order Crank-Nicolson method for time-fractional PDEs. Zbl 1406.65060Gunzburger, Max; Wang, Jilu 8 2019 Convergence of finite element solutions of stochastic partial integro-differential equations driven by white noise. Zbl 1462.65143Gunzburger, Max; Li, Buyang; Wang, Jilu 8 2019 Exponential time differencing for mimetic multilayer Ocean models. Zbl 1453.86019Pieper, Konstantin; Sockwell, K. Chad; Gunzburger, Max 8 2019 An efficient algorithm for simulating ensembles of parameterized flow problems. Zbl 1466.65133Gunzburger, Max; Jiang, Nan; Wang, Zhu 8 2019 Optimally accurate higher-order finite element methods for polytopial approximations of domains with smooth boundaries. Zbl 1417.65186Cheung, James; Perego, Mauro; Bochev, Pavel; Gunzburger, Max 7 2019 A localized reduced-order modeling approach for PDEs with bifurcating solutions. Zbl 1441.65082Hess, Martin; Alla, Alessandro; Quaini, Annalisa; Rozza, Gianluigi; Gunzburger, Max 6 2019 Error analysis of fully discrete finite element approximations to an optimal control problem governed by a time-fractional PDE. Zbl 1417.65171Gunzburger, Max; Wang, Jilu 5 2019 An evolve-filter-relax stabilized reduced order stochastic collocation method for the time-dependent Navier-Stokes equations. Zbl 1428.65029Gunzburger, M.; Iliescu, T.; Mohebujjaman, M.; Schneier, M. 4 2019 Descriptions, discretizations, and comparisons of time/space colored and white noise forcings of the Navier-Stokes equations. Zbl 1421.76156Gunzburger, Max D.; Zhao, Wenju 2 2019 Survey of multifidelity methods in uncertainty propagation, inference, and optimization. Zbl 1458.65003Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 98 2018 On Stokes-Ritz projection and multistep backward differentiation schemes in decoupling the Stokes-Darcy model. Zbl 1465.65094Gunzburger, Max; He, Xiaoming; Li, Buyang 24 2018 A higher-order ensemble/proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1402.35207Gunzburger, Max; Jiang, Nan; Schneier, Michael 11 2018 Weak-Galerkin finite element methods for a second-order elliptic variational inequality. Zbl 1440.65204Guan, Qingguang; Gunzburger, Max; Zhao, Wenju 10 2018 Convergence analysis of multifidelity Monte Carlo estimation. Zbl 1394.35492Peherstorfer, Benjamin; Gunzburger, Max; Willcox, Karen 6 2018 Analysis and approximation of a fractional Laplacian-based closure model for turbulent flows and its connection to Richardson pair dispersion. Zbl 1409.76061Gunzburger, Max; Jiang, Nan; Xu, Feifei 3 2018 An ensemble-proper orthogonal decomposition method for the nonstationary Navier-Stokes equations. Zbl 1394.76067Gunzburger, Max; Jiang, Nan; Schneier, Michael 28 2017 Nonlocal convection-diffusion problems on bounded domains and finite-range jump processes. Zbl 1436.35307D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Richard 13 2017 Analysis and approximation of a nonlocal obstacle problem. Zbl 1353.65064Guan, Qingguang; Gunzburger, Max 7 2017 Comparison of approaches for random PDE optimization problems based on different matching functionals. Zbl 1370.49032Lee, Hyung-Chun; Gunzburger, Max D. 7 2017 Reduced basis methods for nonlocal diffusion problems with random input data. Zbl 1439.74415Guan, Qingguang; Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan 6 2017 Algorithms and analyses for stochastic optimization for turbofan noise reduction using parallel reduced-order modeling. Zbl 1439.76136Yang, Huanhuan; Gunzburger, Max 3 2017 Optimal model management for multifidelity Monte Carlo estimation. Zbl 1351.65009Peherstorfer, Benjamin; Willcox, Karen; Gunzburger, Max 36 2016 An efficient and long-time accurate third-order algorithm for the Stokes-Darcy system. Zbl 1388.76127Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 24 2016 Identification of the diffusion parameter in nonlocal steady diffusion problems. Zbl 1342.49053D’Elia, M.; Gunzburger, M. 15 2016 Asymptotically compatible schemes for the approximation of fractional Laplacian and related nonlocal diffusion problems on bounded domains. Zbl 1356.65239Tian, Xiaochuan; Du, Qiang; Gunzburger, Max 13 2016 Quadrature rules for finite element approximations of 1D nonlocal problems. Zbl 1349.65729Zhang, Xiaoping; Gunzburger, Max; Ju, Lili 7 2016 Hyperspherical sparse approximation techniques for high-dimensional discontinuity detection. Zbl 1386.65083Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max; Burkardt, John 7 2016 A two phase field model for tracking vesicle-vesicle adhesion. Zbl 1366.92019Gu, Rui; Wang, Xiaoqiang; Gunzburger, Max 6 2016 A multiscale method for nonlocal mechanics and diffusion and for the approximation of discontinuous functions. Zbl 1436.74076Xu, Feifei; Gunzburger, Max; Burkardt, John 6 2016 A multiscale implementation based on adaptive mesh refinement for the nonlocal peridynamics model in one dimension. Zbl 1381.74214Xu, Feifei; Gunzburger, Max; Burkardt, John; Du, Qiang 5 2016 Nodal-type collocation methods for hypersingular integral equations and nonlocal diffusion problems. Zbl 1425.65215Zhang, Xiaoping; Gunzburger, Max; Ju, Lili 2 2016 A least-squares finite element method for a nonlinear Stokes problem in glaciology. Zbl 1443.65360Monnesland, Irene Sonja; Lee, Eunjung; Gunzburger, Max; Yoon, Ryeongkyung 1 2016 Fractional diffusion on bounded domains. Zbl 1488.35557Defterli, Ozlem; D’Elia, Marta; Du, Qiang; Gunzburger, Max; Lehoucq, Rich; Meerschaert, Mark M. 48 2015 A multilevel stochastic collocation method for partial differential equations with random input data. Zbl 1327.65014Teckentrup, A. L.; Jantsch, P.; Webster, C. G.; Gunzburger, M. 44 2015 Peridynamics and material interfaces. Zbl 1455.74009Alali, Bacim; Gunzburger, Max 14 2015 \(\theta\) schemes for finite element discretization of the space-time fractional diffusion equations. Zbl 1320.65141Guan, Qingguang; Gunzburger, Max 11 2015 Stability and accuracy of time-stepping schemes and dispersion relations for a nonlocal wave equation. Zbl 1309.65106Guan, Qingguang; Gunzburger, Max 6 2015 Stability and convergence of time-stepping methods for a nonlocal model for diffusion. Zbl 1334.65145Guan, Qingguang; Gunzburger, Max 4 2015 Power-law noises over general spatial domains and on nonstandard meshes. Zbl 1322.65024van Wyk, Hans-Werner; Gunzburger, Max; Burkhardt, John; Stoyanov, Miroslav 4 2015 A generalized nonlocal vector calculus. Zbl 1331.26018Alali, Bacim; Liu, Kuo; Gunzburger, Max 4 2015 A hyperspherical adaptive sparse-grid method for high-dimensional discontinuity detection. Zbl 1317.65058Zhang, G.; Webster, C.; Gunzburger, M.; Burkardt, J. 2 2015 Stochastic finite element methods for partial differential equations with random input data. Zbl 1398.65299Gunzburger, Max D.; Webster, Clayton G.; Zhang, Guannan 80 2014 Parallel, non-iterative, multi-physics domain decomposition methods for time-dependent Stokes-Darcy systems. Zbl 1457.65089Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 78 2014 An adaptive wavelet stochastic collocation method for irregular solutions of partial differential equations with random input data. Zbl 1316.65011Gunzburger, Max; Webster, Clayton G.; Zhang, Guannan 18 2014 Optimal distributed control of nonlocal steady diffusion problems. Zbl 1298.49006D’Elia, Marta; Gunzburger, Max 15 2014 Peridynamic state-based models and the embedded-atom model. Zbl 1373.82029Seleson, Pablo; Parks, Michael L.; Gunzburger, Max 14 2014 Simulating vesicle-substrate adhesion using two phase field functions. Zbl 1349.92050Gu, R.; Wang, X.; Gunzburger, M. 7 2014 An adaptive sparse-grid iterative ensemble Kalman filter approach for parameter field estimation. Zbl 1383.76393Webster, Clayton G.; Zhang, Guannan; Gunzburger, Max 4 2014 An efficient and accurate method for the identification of the most influential random parameters appearing in the input data for PDEs. Zbl 1426.76634Labovsky, A.; Gunzburger, Max 4 2014 Goal-oriented a posteriori error estimation for finite volume methods. Zbl 1293.65116Chen, Qingshan; Gunzburger, Max 3 2014 Finite element three-dimensional Stokes ice sheet dynamics model with enhanced local mass conservation. Zbl 1351.86030Leng, 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 1373.86004Leng, 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 1266.26020Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 168 2013 The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator. Zbl 1345.35128D’Elia, Marta; Gunzburger, Max 91 2013 Efficient and long-time accurate second-order methods for the Stokes-Darcy system. Zbl 1282.76094Chen, Wenbin; Gunzburger, Max; Sun, Dong; Wang, Xiaoming 51 2013 Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. Zbl 1277.35007Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 34 2013 Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Zbl 1286.74010Seleson, Pablo; Gunzburger, Max; Parks, Michael L. 30 2013 A sparse-grid method for multi-dimensional backward stochastic differential equations. Zbl 1289.65011Zhang, Guannan; Gunzburger, Max; Zhao, Weidong 19 2013 A co-volume scheme for the rotating shallow water equations on conforming non-orthogonal grids. Zbl 1426.76346Chen, Qingshan; Ringler, Todd; Gunzburger, Max 10 2013 Coarse-grid sampling interpolatory methods for approximating Gaussian random fields. Zbl 1401.60094D’Elia, Marta; Gunzburger, Max 5 2013 Well-posedness results for a nonlinear Stokes problem arising in glaciology. Zbl 1282.35292Chen, Qingshan; Gunzburger, Max; Perego, Mauro 5 2013 A distributed control approach for the boundary optimal control of the steady MHD equations. Zbl 1373.76339Bornia, G.; Gunzburger, M.; Manservisi, S. 4 2013 Unified matching grids for multidomain multiphysics simulations. Zbl 1285.65081Womeldorff, G.; Peterson, J.; Gunzburger, M.; Ringler, T. 1 2013 Analysis and approximation of nonlocal diffusion problems with volume constraints. Zbl 1422.76168Du, Qiang; Gunzburger, Max; Lehoucq, R. B.; Zhou, Kun 239 2012 Error analysis of a stochastic collocation method for parabolic partial differential equations with random input data. Zbl 1260.65007Zhang, Guannan; Gunzburger, Max 15 2012 High accuracy method for turbulent flow problems. Zbl 1437.76039Gunzburger, M.; Labovsky, A. 13 2012 A parallel Robin-Robin domain decomposition method for the Stokes-Darcy system. Zbl 1414.76017Chen, Wenbin; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 79 2011 Robin-Robin domain decomposition methods for the steady-state Stokes-Darcy system with the Beavers-Joseph interface condition. Zbl 1305.76072Cao, Yanzhao; Gunzburger, Max; He, Xiaoming; Wang, Xiaoming 73 2011 Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Zbl 1225.74082Chen, X.; Gunzburger, Max 69 2011 Error estimates of stochastic optimal Neumann boundary control problems. Zbl 1243.65008Gunzburger, Max D.; Lee, Hyung-Chun; Lee, Jangwoon 30 2011 Analysis and finite element approximation of a coupled, continuum pipe-flow/Darcy model for flow in porous media with embedded conduits. Zbl 1282.76172Cao, Yanzhao; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 14 2011 Space-time adaptive wavelet methods for optimal control problems constrained by parabolic evolution equations. Zbl 1232.65099Gunzburger, Max D.; Kunoth, Angela 13 2011 Optimal control of stochastic flow over a backward-facing step using reduced-order modeling. Zbl 1232.93097Gunzburger, Max; Ming, Ju 9 2011 Analysis of finite element discretizations of an optimal control formulation of the image registration problem. Zbl 1254.65036Lee, Eunjung; Gunzburger, Max 7 2011 Coupled models and parallel simulations for three-dimensional full-Stokes ice sheet modeling. Zbl 1265.76046Zhang, Huai; Ju, Lili; Gunzburger, Max; Ringler, Todd; Price, Stephen 4 2011 Effects of approximate deconvolution models on the solution of the stochastic Navier-Stokes equations. Zbl 1249.65209Gunzburger, M.; Labovsky, A. 3 2011 Pink noise, \(1/f^\alpha\) noise, and their effect on solutions of differential equations. Zbl 1229.65028Stoyanov, Miro; Gunzburger, Max; Burkardt, John 2 2011 Coupled Stokes-Darcy model with Beavers-Joseph interface boundary condition. Zbl 1189.35244Cao, Yanzhao; Gunzburger, Max; Hua, Fei; Wang, Xiaoming 109 2010 Finite element approximations for Stokes-Darcy flow with Beavers-Joseph interface conditions. Zbl 1252.76040Cao, Yanzhao; Gunzburger, Max; Hu, Xiaolong; Hua, Fei; Wang, Xiaoming; Zhao, Weidong 106 2010 A nonlocal vector calculus with application to nonlocal boundary value problems. Zbl 1210.35057Gunzburger, Max; Lehoucq, R. B. 67 2010 Asymptotic analysis of the differences between the Stokes-Darcy system with different interface conditions and the Stokes-Brinkman system. Zbl 1352.35093Chen, Nan; Gunzburger, Max; Wang, Xiaoming 35 2010 Superconvergence analysis of FEMs for the Stokes-Darcy system. Zbl 1303.76086Chen, Wenbin; Chen, Puying; Gunzburger, Max; Yan, Ningning 21 2010 Advances in studies and applications of centroidal Voronoi tessellations. Zbl 1224.52032Du, Qiang; Gunzburger, Max; Ju, Lili 21 2010 A quadrature-rule type approximation to the quasi-continuum method. Zbl 1188.70046Gunzburger, Max; Zhang, Yanzhi 12 2010 ...and 176 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 4,944 Authors 129 Gunzburger, Max D. 87 Du, Qiang 52 He, Yinnian 45 Li, Jian 44 Ju, Lili 38 Rozza, Gianluigi 30 Bochev, Pavel B. 30 Hou, Yanren 30 Huang, Pengzhan 29 Feng, Xinlong 27 Chen, Zhangxin 27 Layton, William J. 26 Luo, Zhendong 25 He, Xiaoming 23 Yang, Suh-Yuh 23 Zheng, Haibiao 22 Protas, Bartosz 22 Tian, Xiaochuan 22 Wang, Zhu 20 Chen, Yanping 19 D’Elia, Marta 19 Gerritsma, Marc I. 19 Lee, Hyung-Chun 18 Takahashi, Takéo 18 Wang, Hong 17 Iliescu, Traian 17 Navon, Ionel Michael 17 Pan, Xingbin 17 Si, Zhiyong 16 Huang, Yunqing 16 Lee, Hyesuk Kwon 15 Zhang, Guodong 14 Manzoni, Andrea 14 Peherstorfer, Benjamin 14 Quarteroni, Alfio M. 14 Su, Haiyan 14 Webster, Clayton G. 13 Feng, Minfu 13 Mei, Liquan 13 Ravindran, Sivaguru S. 13 Trenchea, Catalin 13 Wang, Xiaoming 13 Warma, Mahamadi 13 Zuo, Liyun 12 Alekseev, Gennady V. 12 An, Rong 12 Chrysafinos, Konstantinos 12 Codina, Ramon 12 Lu, Zuliang 12 Manservisi, Sandro 12 Rebholz, Leo G. 12 Shadid, John N. 12 Turkel, Eli L. 11 Al Mahbub, Md. Abdullah 11 Antoine, Xavier 11 Ballarin, Francesco 11 Burkardt, John V. 11 Du, Guangzhi 11 Ervin, Vincent J. 11 Jiang, Bo-Nan 11 Kunisch, Karl 11 Lee, Eunjung 11 Lehoucq, Richard B. 11 Li, Buyang 11 Liu, Steve Wenbin 11 Meir, Amnon J. 11 Mengesha, Tadele 11 Muha, Boris 11 Otárola, Enrique 11 Peterson, Janet S. 11 Rossi, Julio Daniel 11 Shang, Yueqiang 11 Singler, John R. 11 Tröltzsch, Fredi 10 Barrenechea, Gabriel R. 10 Chen, Wenbin 10 Dassi, Franco 10 Deng, Weihua 10 Foster, John T. jun. 10 Ghattas, Omar N. 10 Jiang, Nan 10 Khan, Akhtar Ali 10 Nobile, Fabio 10 Pedregal, Pablo 10 Reddy, Junuthula Narasimha 10 Shan, Li 10 Shi, Feng 10 Willcox, Karen E. 10 Yang, Xiaofeng 10 Yu, Yue 10 Zhao, Xin 9 Barucq, Hélène 9 Bellido, José Carlos 9 Čanić, Sunčica 9 Cao, Yanzhao 9 Carey, Graham Francis 9 Carstensen, Carsten 9 Chang, Ching Lung 9 Chen, Gang 9 Djellouli, Rabia ...and 4,844 more Authors all top 5 Cited in 374 Serials 368 Computer Methods in Applied Mechanics and Engineering 288 Journal of Computational Physics 200 Computers & Mathematics with Applications 149 Journal of Computational and Applied Mathematics 143 Journal of Scientific Computing 125 Applied Mathematics and Computation 103 Applied Numerical Mathematics 91 SIAM Journal on Scientific Computing 81 SIAM Journal on Numerical Analysis 73 Journal of Mathematical Analysis and Applications 67 International Journal for Numerical Methods in Engineering 67 Numerische Mathematik 56 Mathematics of Computation 55 Computers and Fluids 55 Numerical Methods for Partial Differential Equations 51 Computational Mechanics 47 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 46 International Journal for Numerical Methods in Fluids 46 SIAM/ASA Journal on Uncertainty Quantification 39 Journal of Fluid Mechanics 38 Numerical Functional Analysis and Optimization 38 Advances in Computational Mathematics 35 Nonlinear Analysis. 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Académie des Sciences, Paris 6 Automatica 6 Journal of Functional Analysis 6 Mathematical and Computer Modelling ...and 274 more Serials all top 5 Cited in 53 Fields 2,322 Numerical analysis (65-XX) 1,699 Fluid mechanics (76-XX) 1,581 Partial differential equations (35-XX) 538 Mechanics of deformable solids (74-XX) 477 Calculus of variations and optimal control; optimization (49-XX) 192 Statistical mechanics, structure of matter (82-XX) 188 Probability theory and stochastic processes (60-XX) 161 Systems theory; control (93-XX) 103 Computer science (68-XX) 102 Statistics (62-XX) 102 Optics, electromagnetic theory (78-XX) 101 Integral equations (45-XX) 85 Operations research, mathematical programming (90-XX) 82 Biology and other natural sciences (92-XX) 75 Operator theory (47-XX) 72 Geophysics (86-XX) 62 Classical thermodynamics, heat transfer (80-XX) 56 Real functions (26-XX) 53 Ordinary differential equations (34-XX) 44 Approximations and expansions (41-XX) 42 Functional analysis (46-XX) 32 Linear and multilinear algebra; matrix theory (15-XX) 32 Dynamical systems and ergodic theory (37-XX) 29 Global analysis, analysis on manifolds (58-XX) 28 Information and communication theory, circuits (94-XX) 27 Mechanics of particles and systems (70-XX) 27 Quantum theory (81-XX) 18 Harmonic analysis on Euclidean spaces (42-XX) 18 Convex and discrete geometry (52-XX) 17 Combinatorics (05-XX) 14 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Measure and integration (28-XX) 11 Special functions (33-XX) 10 General and overarching topics; collections (00-XX) 10 Differential geometry (53-XX) 7 Potential theory (31-XX) 4 Difference and functional equations (39-XX) 3 History and biography (01-XX) 3 Integral transforms, operational calculus (44-XX) 3 Astronomy and astrophysics (85-XX) 3 Mathematics education (97-XX) 2 Mathematical logic and foundations (03-XX) 2 Number theory (11-XX) 2 Functions of a complex variable (30-XX) 2 Geometry (51-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Topological groups, Lie groups (22-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 Manifolds and cell complexes (57-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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