Edit Profile (opens in new tab) Brenner, Susanne Cecelia Compute Distance To: Compute Author ID: brenner.susanne-c Published as: Brenner, Susanne C.; Brenner, S. C.; Brenner, Susanne; Brenner, Susanne Cecelia more...less Homepage: https://www.math.lsu.edu/~brenner/ External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 137 Publications since 1989, including 3 Books 8 Contributions as Editor Co-Authors: 59 Co-Authors with 91 Joint Publications 2,469 Co-Co-Authors all top 5 Co-Authors 38 single-authored 8 Gudi, Thirupathi 7 Cui, Jintao 7 Zhang, Yi 6 Davis, Christopher B. 6 Gedicke, Joscha 5 Li, Fengyan 5 Neilan, Michael 5 Owens, Luke 4 Barker, Andrew T. 4 Park, Eunhee 4 Wang, Kening 3 Oh, Duk-Soon 3 Scott, Larkin Ridgway 3 Tan, Zhiyu 3 Zhang, Hongchao 2 Carstensen, Carsten 2 Diegel, Amanda E. 2 Garay, José C. 2 Li, Hengguang 2 Liu, Sijing 2 Monk, Peter B. 2 Oh, Minah 2 Porwal, Kamana 2 Sun, Jiguang 2 Szyld, Daniel B. 2 Wollner, Winnifried 2 Zhao, Jie 1 Antonietti, Paola Francesca 1 Ayuso de Dios, Blanca 1 Ben Belgacem, Faker 1 Bjørstad, Petter Erling 1 Bunde, Armin 1 Cai, Xiao-Chuan 1 Çeşmelioğlu, Ayçıl 1 Demkowicz, Leszek F. 1 Gander, Martin Jakob 1 Govindan, R. B. 1 Gu, Shiyuan 1 Guan, Qingguang 1 Halpern, Lawrence 1 Havlin, Shlomo 1 He, Qingmi 1 Hoppe, Ronald H. W. 1 Kawecki, Ellya L. 1 Kim, Hyea Hyun 1 Klawonn, Axel 1 Kornhuber, Ralf 1 Leykekhman, Dmitriy 1 Pollock, Sara 1 Rahman, Talal 1 Reiser, Armin 1 Rivière, Beatrice M. 1 Sarkis, Marcus V. 1 Schedensack, Mira 1 Schellnhuber, Hans-Joachim 1 Sharma, Natasha S. 1 Shparlinski, Igor E. 1 Shu, Chi-Wang 1 Vexler, Boris 1 Vjushin, Dmitry 1 Wang, Zhuo 1 Widlund, Olof B. 1 Wriggers, Peter 1 Xu, Yuesheng all top 5 Serials 16 Mathematics of Computation 13 Numerische Mathematik 12 SIAM Journal on Numerical Analysis 11 Journal of Scientific Computing 10 ETNA. Electronic Transactions on Numerical Analysis 7 Journal of Computational and Applied Mathematics 6 Computational Methods in Applied Mathematics 4 Computer Methods in Applied Mechanics and Engineering 4 Oberwolfach Reports 3 Numerical Functional Analysis and Optimization 3 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 3 Numerical Linear Algebra with Applications 3 Texts in Applied Mathematics 2 IMA Journal of Numerical Analysis 2 Calcolo 2 Applied Numerical Mathematics 2 SIAM Journal on Scientific Computing 2 Results in Applied Mathematics 1 Computers & Mathematics with Applications 1 Houston Journal of Mathematics 1 Mathematical Methods in the Applied Sciences 1 Physica A 1 BIT 1 SIAM Journal on Control and Optimization 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Numerical Methods for Partial Differential Equations 1 Applied Mathematics Letters 1 East-West Journal of Numerical Mathematics 1 Advances in Computational Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Wuhan University Journal of Natural Sciences (WUJNS) 1 Optimization and Engineering 1 The ANZIAM Journal 1 Journal of Numerical Mathematics 1 ANACM. Applied Numerical Analysis and Computational Mathematics 1 International Journal of Numerical Analysis and Modeling 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Contemporary Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Computational Science and Engineering 1 JNAIAM. Journal of Numerical Analysis, Industrial and Applied Mathematics all top 5 Fields 137 Numerical analysis (65-XX) 66 Partial differential equations (35-XX) 26 Mechanics of deformable solids (74-XX) 20 Calculus of variations and optimal control; optimization (49-XX) 11 Optics, electromagnetic theory (78-XX) 9 Fluid mechanics (76-XX) 7 General and overarching topics; collections (00-XX) 4 Functional analysis (46-XX) 3 Potential theory (31-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 History and biography (01-XX) 2 Operations research, mathematical programming (90-XX) 1 Number theory (11-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) 1 Approximations and expansions (41-XX) 1 Geophysics (86-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 126 Publications have been cited 5,023 times in 3,609 Documents Cited by ▼ Year ▼ The mathematical theory of finite element methods. 3rd ed. Zbl 1135.65042Brenner, Susanne C.; Scott, L. Ridgway 1,266 2008 The mathematical theory of finite element methods. Zbl 0804.65101Brenner, Susanne C.; Scott, L. Ridgway 942 1994 The mathematical theory of finite element methods. 2nd ed. Zbl 1012.65115Brenner, Susanne C.; Scott, L. Ridgway 455 2002 Poincaré–Friedrichs inequalities for piecewise \(H^{1}\) functions. Zbl 1045.65100Brenner, Susanne C. 225 2003 \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains. Zbl 1071.65151Brenner, Susanne C.; Sung, Li-Yeng 157 2005 Korn’s inequalities for piecewise \(H^1\) vector fields. Zbl 1055.65118Brenner, Susanne C. 147 2004 Linear finite element methods for planar linear elasticity. Zbl 0766.73060Brenner, Susanne C.; Sung, Li-Yeng 103 1992 Virtual element methods on meshes with small edges or faces. Zbl 1393.65049Brenner, Susanne C.; Sung, Li-Yeng 66 2018 Two-level additive Schwarz preconditioners for nonconforming finite element methods. Zbl 0859.65124Brenner, Susanne C. 62 1996 Some estimates for virtual element methods. Zbl 1434.65237Brenner, Susanne C.; Guan, Qingguang; Sung, Li-Yeng 49 2017 \(\mathcal{C}^{0}\) penalty methods for the fully nonlinear Monge-Ampère equation. Zbl 1228.65220Brenner, Susanne C.; Gudi, Thirupathi; Neilan, Michael; Sung, Li-Yeng 48 2011 BDDC and FETI-DP without matrices or vectors. Zbl 1173.65363Brenner, Susanne C.; Sung, Li-Yeng 47 2007 A weakly over-penalized symmetric interior penalty method. Zbl 1171.65077Brenner, Susanne C.; Owens, Luke; Sung, Li-Yeng 44 2008 An optimal-order multigrid method for P1 nonconforming finite elements. Zbl 0664.65103Brenner, Susanne C. 41 1989 Convergence of nonconforming multigrid methods without full elliptic regularity. Zbl 0912.65099Brenner, Susanne C. 40 1999 An a posteriori error estimator for a quadratic \(C^{0}\)-interior penalty method for the biharmonic problem. Zbl 1201.65197Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 40 2010 A two-level additive Schwarz preconditioner for nonconforming plate elements. Zbl 0855.73071Brenner, Susanne C. 36 1996 A locally divergence-free interior penalty method for two-dimensional curl-curl problems. Zbl 1168.65068Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 35 2008 Multigrid methods for the computation of singular solutions and stress intensity factors. I: Corner singularities. Zbl 1043.65136Brenner, Susanne C. 33 1999 A multigrid algorithm for the lowest-order Raviart-Thomas mixed triangular finite element method. Zbl 0759.65080Brenner, Susanne C. 33 1992 A quadratic \(C^0\) interior penalty method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1263.65110Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Hongchao; Zhang, Yi 32 2012 A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations. Zbl 1126.78017Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 32 2007 Poincaré–Friedrichs inequalities for piecewise \(H^2\) functions. Zbl 1072.65147Brenner, Susanne C.; Wang, Kening; Zhao, Jie 30 2004 Convergence of multigrid algorithms for interior penalty methods. Zbl 1073.65117Brenner, Susanne C.; Zhao, Jie 30 2005 An optimal-order nonconforming multigrid method for the biharmonic equation. Zbl 0679.65083Brenner, Susanne C. 30 1989 A \(\mathcal C^0\) interior penalty method for a fourth order elliptic singular perturbation problem. Zbl 1225.65108Brenner, Susanne C.; Neilan, Michael 29 2011 A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1290.65108Brenner, Susanne C.; Sung, Li-yeng; Zhang, Hongchao; Zhang, Yi 29 2013 Forty years of the Crouzeix-Raviart element. Zbl 1310.65142Brenner, Susanne C. 28 2015 Finite element methods for the displacement obstacle problem of clamped plates. Zbl 1250.74023Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Yi 27 2012 \(C^{0}\) interior penalty methods. Zbl 1248.65120Brenner, Susanne C. 27 2012 \(C^0\) Interior penalty Galerkin method for biharmonic eigenvalue problems. Zbl 1349.65439Brenner, Susanne C.; Monk, Peter; Sun, Jiguang 25 2015 A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem. Zbl 1166.78006Brenner, S. C.; Cui, J.; Li, F.; Sung, L.-Y. 25 2008 The condition number of the Schur complement in domain decomposition. Zbl 0936.65141Brenner, Susanne C. 24 1999 A nonconforming mixed multigrid method for the pure displacement problem in planar linear elasticity. Zbl 0767.73068Brenner, Susanne C. 24 1993 Multigrid methods for the symmetric interior penalty method on graded meshes. Zbl 1224.65288Brenner, S. C.; Cui, J.; Sung, L.-Y. 23 2009 Multigrid methods for parameter dependent problems. Zbl 0848.73062Brenner, Susanne C. 22 1996 Hodge decomposition methods for a quad-curl problem on planar domains. Zbl 1398.65290Brenner, Susanne C.; Sun, Jiguang; Sung, Li-yeng 21 2017 A \(C^0\) interior penalty method for a von Kármán plate. Zbl 1457.65181Brenner, Susanne C.; Neilan, Michael; Reiser, Armin; Sung, Li-Yeng 21 2017 An adaptive \(P_1\) finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions. Zbl 1373.78416Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 19 2016 Convergence of the multigrid \(V\)-cycle algorithm for second-order boundary value problems without full elliptic regularity. Zbl 0990.65121Brenner, Susanne C. 19 2002 Finite element approximations of the three dimensional Monge-Ampère equation. Zbl 1272.65088Brenner, Susanne Cecelia; Neilan, Michael 19 2012 Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell’s equations. Zbl 1274.78089Brenner, S. C.; Cui, J.; Nan, Z.; Sung, L.-Y. 19 2012 A new convergence analysis of finite element methods for elliptic distributed optimal control problems with pointwise state constraints. Zbl 1370.49006Brenner, Susanne C.; Sung, Li-yeng 18 2017 Convergence of nonconforming \(V\)-cycle and \(F\)-cycle multigrid algorithms for second order elliptic boundary value problems. Zbl 1052.65102Brenner, Susanne C. 18 2004 A nonconforming multigrid method for the stationary Stokes equations. Zbl 0705.76027Brenner, Susanne C. 18 1990 A quadratic \(C^0\) interior penalty method for an elliptic optimal control problem with state constraints. Zbl 1282.65074Brenner, S. C.; Sung, L.-Y.; Zhang, Y. 17 2014 A partition of unity method for a class of fourth order elliptic variational inequalities. Zbl 1425.65070Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng 16 2014 Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods. Zbl 1088.65108Brenner, Susanne C.; Wang, Kening 16 2005 Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes. Zbl 1229.65224Brenner, S. C.; Cui, J.; Gudi, T.; Sung, L.-Y. 15 2011 Balancing domain decomposition for nonconforming plate elements. Zbl 0937.74060Brenner, Susanne C.; Sung, Li-yeng 15 1999 A quadratic \(C^0\) interior penalty method for linear fourth order boundary value problems with boundary conditions of the Cahn-Hilliard type. Zbl 1256.65101Brenner, Susanne C.; Gu, Shiyuan; Gudi, Thirupathi; Sung, Li-Yeng 15 2012 A \(W\)-cycle algorithm for a weakly over-penalized interior penalty method. Zbl 1173.65368Brenner, Susanne C.; Owens, Luke 15 2007 Hodge decomposition for two-dimensional time-harmonic Maxwell’s equations: impedance boundary condition. Zbl 1361.78007Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 14 2017 A weakly over-penalized symmetric interior penalty method for the biharmonic problem. Zbl 1205.65311Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 14 2010 A weakly over-penalized non-symmetric interior penalty method. Zbl 1145.65095Brenner, Susanne C.; Owens, Luke 14 2007 Multigrid algorithms for \(C^0\) interior penalty methods. Zbl 1114.65151Brenner, Susanne C.; Sung, Li-yeng 14 2006 Higher order weakly over-penalized symmetric interior penalty methods. Zbl 1273.65174Brenner, Susanne C.; Owens, Luke; Sung, Li-Yeng 13 2012 A nonconforming mixed multigrid method for the pure traction problem in planar linear elasticity. Zbl 0809.73064Brenner, Susanne C. 13 1994 Two-level additive Schwarz preconditioners for nonconforming finite elements. Zbl 0817.65107Brenner, Susanne C. 13 1994 Two-level additive Schwarz preconditioners for a weakly over-penalized symmetric interior penalty method. Zbl 1230.65124Barker, A. T.; Brenner, S. C.; Park, E.-H.; Sung, L.-Y. 12 2011 A posteriori error control for a weakly over-penalized symmetric interior penalty method. Zbl 1203.65230Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 12 2009 An intrinsically parallel finite element method. Zbl 1203.65244Brenner, S. C.; Gudi, T.; Owens, L.; Sung, L.-Y. 12 2010 Schwarz methods for a preconditioned WOPSIP method for elliptic problems. Zbl 1284.65162Antonietti, Paola F.; Ayuso de Dios, Blanca; Brenner, Susanne C.; Sung, Li-yeng 12 2012 Isoparametric \(C ^{0}\) interior penalty methods for plate bending problems on smooth domains. Zbl 1341.74147Brenner, Susanne C.; Neilan, Michael; Sung, Li-Yeng 11 2013 Some nonstandard finite element estimates with applications to \(3D\) Poisson and Signorini problems. Zbl 0981.65131Ben Belgacem, Faker; Brenner, Susanne C. 11 2001 Multigrid methods for the computation of singular solutions and stress intensity factors. II: Crack singularities. Zbl 0890.73060Brenner, S. C.; Sung, L.-Y. 11 1997 A \(C^0\) interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints. Zbl 1384.65038Brenner, Susanne C.; Oh, Minah; Pollock, Sara; Porwal, Kamana; Schedensack, Mira; Sharma, Natasha S. 11 2016 A nonconforming penalty method for a two-dimensional curl-curl problem. Zbl 1168.78315Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 10 2009 Multigrid methods for saddle point problems: Stokes and Lamé systems. Zbl 1298.76067Brenner, Susanne C.; Li, Hengguang; Sung, Li-Yeng 10 2014 A balancing domain decomposition by constraints preconditioner for a weakly over-penalized symmetric interior penalty method. Zbl 1313.65049Brenner, Susanne C.; Park, Eun-Hee; Sung, Li-Yeng 10 2013 A Morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints. Zbl 1412.49025Brenner, Susanne C.; Gudi, Thirupathi; Porwal, Kamana; Sung, Li-Yeng 10 2018 \(C^0\) interior penalty methods for an elliptic state-constrained optimal control problem with Neumann boundary condition. Zbl 07006472Brenner, Susanne C.; Sung, Li-yeng; Zhang, Yi 10 2019 Nonconforming Maxwell eigensolvers. Zbl 1203.65236Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 9 2009 Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions. Zbl 1065.65128Brenner, Susanne C. 9 2004 \(C^0\) interior penalty methods for an elliptic distributed optimal control problem on nonconvex polygonal domains with pointwise state constraints. Zbl 1396.49003Brenner, Susanne C.; Gedicke, Joscha; Sung, Li-yeng 9 2018 Virtual enriching operators. Zbl 1471.65192Brenner, Susanne C.; Sung, Li-Yeng 8 2019 An a posteriori analysis of \(C^0\) interior penalty methods for the obstacle problem of clamped Kirchhoff plates. Zbl 1381.74129Brenner, Susanne C.; Gedicke, Joscha; Sung, Li-Yeng; Zhang, Yi 8 2017 Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework. Zbl 1065.65136Brenner, Susanne 8 2003 Adaptive \(C^0\) interior penalty methods for Hamilton-Jacobi-Bellman equations with cordes coefficients. Zbl 1458.65145Brenner, Susanne C.; Kawecki, Ellya L. 7 2021 Overcoming corner singularities using multigrid methods. Zbl 0914.65117Brenner, Susanne C. 7 1998 Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems. Zbl 1232.65164Barker, A. T.; Brenner, S. C.; Sung, L.-Y. 7 2011 An adaptive \(P_1\) finite element method for two-dimensional Maxwell’s equations. Zbl 1266.78027Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 7 2013 A partition of unity method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1293.74424Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng 7 2014 Post-processing procedures for an elliptic distributed optimal control problem with pointwise state constraints. Zbl 1320.65169Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Yi 7 2015 Multigrid methods based on Hodge decomposition for a quad-curl problem. Zbl 1420.65119Brenner, Susanne C.; Cui, Jintao; Sung, Li-yeng 7 2019 A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach. Zbl 1306.65276Barker, Andrew T.; Brenner, Susanne C. 6 2014 Lower bounds for two-level additive Schwarz preconditioners with small overlap. Zbl 0959.65062Brenner, Susanne C. 6 2000 A robust solver for a mixed finite element method for the Cahn-Hilliard equation. Zbl 1407.65179Brenner, Susanne C.; Diegel, Amanda E.; Sung, Li-Yeng 6 2018 \(P_1\) finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditions. Zbl 1443.49007Brenner, S. C.; Oh, M.; Sung, L.-Y. 5 2020 A quadratic nonconforming vector finite element for \(H(\text{curl}; \varOmega)\cap H(\text{div}; \varOmega)\). Zbl 1170.65091Brenner, Susanne C.; Sung, Li-Yeng 4 2009 Multigrid methods for the computation of singular solutions and stress intensity factors. III: Interface singularities. Zbl 1054.74047Brenner, Susanne C.; Sung, Li-yeng 4 2003 A one-level additive Schwarz preconditioner for a discontinuous Petrov-Galerkin method. Zbl 1382.65432Barker, Andrew T.; Brenner, Susanne C.; Park, Eun-Hee; Sung, Li-Yeng 4 2014 Preconditioning complicated finite elements by simple finite elements. Zbl 0857.65114Brenner, Susanne C. 4 1996 A nonconforming finite element method for an acoustic fluid-structure interaction problem. Zbl 1456.65148Brenner, Susanne C.; Çeşmelioǧlu, Ayçıl; Cui, Jintao; Sung, Li-Yeng 3 2018 \(P_1\) finite element methods for an elliptic optimal control problem with pointwise state constraints. Zbl 1464.65061Brenner, Susanne C.; Sung, Li-yeng; Gedicke, Joscha 3 2020 An additive analysis of multiplicative Schwarz methods. Zbl 1271.65147Brenner, Susanne C. 3 2013 Multigrid methods for saddle point problems: Oseen system. Zbl 1402.65176Brenner, Susanne C.; Li, Hengguang; Sung, Li-yeng 3 2017 A two-level additive Schwarz preconditioner for macro-element approximations of the plate bending problem. Zbl 0838.73069Brenner, Susanne C. 3 1995 Lower bounds for nonoverlapping domain decomposition preconditioners in two dimensions. Zbl 0974.65114Brenner, Susanne C.; Sung, Li-Yeng 3 2000 An iterative substructuring algorithm for a \(C^{0}\) interior penalty method. Zbl 1321.65181Brenner, Susanne C.; Wang, Kening 3 2012 Adaptive \(C^0\) interior penalty methods for Hamilton-Jacobi-Bellman equations with cordes coefficients. Zbl 1458.65145Brenner, Susanne C.; Kawecki, Ellya L. 7 2021 Additive Schwarz preconditioners for a localized orthogonal decomposition method. Zbl 1473.65337Brenner, Susanne C.; Garay, José C.; Sung, Li-Yeng 1 2021 A \(C^1\) virtual element method for an elliptic distributed optimal control problem with pointwise state constraints. Zbl 1478.65115Brenner, Susanne C.; Sung, Li-Yeng; Tan, Zhiyu 1 2021 \(P_1\) finite element methods for an elliptic state-constrained distributed optimal control problem with Neumann boundary conditions. Zbl 1443.49007Brenner, S. C.; Oh, M.; Sung, L.-Y. 5 2020 \(P_1\) finite element methods for an elliptic optimal control problem with pointwise state constraints. Zbl 1464.65061Brenner, Susanne C.; Sung, Li-yeng; Gedicke, Joscha 3 2020 A robust solver for a second order mixed finite element method for the Cahn-Hilliard equation. Zbl 1478.65080Brenner, Susanne C.; Diegel, Amanda E.; Sung, Li-Yeng 3 2020 A cubic \(C^{\mathbf{0}}\) interior penalty method for elliptic distributed optimal control problems with pointwise state and control constraints. Zbl 1464.49021Brenner, Susanne C.; Sung, Li-yeng; Tan, Zhiyu 1 2020 A one dimensional elliptic distributed optimal control problem with pointwise derivative constraints. Zbl 1447.49001Brenner, Susanne C.; Sung, Li-yeng; Wollner, Winnifried 1 2020 Finite element methods for elliptic distributed optimal control problems with pointwise state constraints (survey). Zbl 1440.49037Brenner, Susanne C. 1 2020 Multigrid methods for saddle point problems: optimality systems. Zbl 1433.49003Brenner, Susanne C.; Liu, Sijing; Sung, Li-yeng 1 2020 \(C^0\) interior penalty methods for an elliptic state-constrained optimal control problem with Neumann boundary condition. Zbl 07006472Brenner, Susanne C.; Sung, Li-yeng; Zhang, Yi 10 2019 Virtual enriching operators. Zbl 1471.65192Brenner, Susanne C.; Sung, Li-Yeng 8 2019 Multigrid methods based on Hodge decomposition for a quad-curl problem. Zbl 1420.65119Brenner, Susanne C.; Cui, Jintao; Sung, Li-yeng 7 2019 Virtual element methods on meshes with small edges or faces. Zbl 1393.65049Brenner, Susanne C.; Sung, Li-Yeng 66 2018 A Morley finite element method for an elliptic distributed optimal control problem with pointwise state and control constraints. Zbl 1412.49025Brenner, Susanne C.; Gudi, Thirupathi; Porwal, Kamana; Sung, Li-Yeng 10 2018 \(C^0\) interior penalty methods for an elliptic distributed optimal control problem on nonconvex polygonal domains with pointwise state constraints. Zbl 1396.49003Brenner, Susanne C.; Gedicke, Joscha; Sung, Li-yeng 9 2018 A robust solver for a mixed finite element method for the Cahn-Hilliard equation. Zbl 1407.65179Brenner, Susanne C.; Diegel, Amanda E.; Sung, Li-Yeng 6 2018 A nonconforming finite element method for an acoustic fluid-structure interaction problem. Zbl 1456.65148Brenner, Susanne C.; Çeşmelioǧlu, Ayçıl; Cui, Jintao; Sung, Li-Yeng 3 2018 Multigrid methods for saddle point problems: Darcy systems. Zbl 1408.76361Brenner, Susanne C.; Oh, Duk-Soon; Sung, Li-Yeng 3 2018 Multigrid methods for \(H(\text{div})\) in three dimensions with nonoverlapping domain decomposition smoothers. Zbl 06987013Brenner, Susanne C.; Oh, Duk-Soon 1 2018 Additive Schwarz preconditioners for the obstacle problem of clamped Kirchhoff plates. Zbl 1408.65084Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-Yeng 1 2018 Some estimates for virtual element methods. Zbl 1434.65237Brenner, Susanne C.; Guan, Qingguang; Sung, Li-Yeng 49 2017 Hodge decomposition methods for a quad-curl problem on planar domains. Zbl 1398.65290Brenner, Susanne C.; Sun, Jiguang; Sung, Li-yeng 21 2017 A \(C^0\) interior penalty method for a von Kármán plate. Zbl 1457.65181Brenner, Susanne C.; Neilan, Michael; Reiser, Armin; Sung, Li-Yeng 21 2017 A new convergence analysis of finite element methods for elliptic distributed optimal control problems with pointwise state constraints. Zbl 1370.49006Brenner, Susanne C.; Sung, Li-yeng 18 2017 Hodge decomposition for two-dimensional time-harmonic Maxwell’s equations: impedance boundary condition. Zbl 1361.78007Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 14 2017 An a posteriori analysis of \(C^0\) interior penalty methods for the obstacle problem of clamped Kirchhoff plates. Zbl 1381.74129Brenner, Susanne C.; Gedicke, Joscha; Sung, Li-Yeng; Zhang, Yi 8 2017 Multigrid methods for saddle point problems: Oseen system. Zbl 1402.65176Brenner, Susanne C.; Li, Hengguang; Sung, Li-yeng 3 2017 A two-level additive Schwarz domain decomposition preconditioner for a flat-top partition of unity method. Zbl 1404.65299Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-Yeng 1 2017 A BDDC preconditioner for a symmetric interior penalty Galerkin method. Zbl 1368.65230Brenner, Susanne C.; Park, Eun-Hee; Sung, Li-Yeng 1 2017 A finite element method for the one-dimensional prescribed curvature problem. Zbl 1380.65361Brenner, Susanne C.; Sung, Li-Yeng; Wang, Zhuo; Xu, Yuesheng 1 2017 An adaptive \(P_1\) finite element method for two-dimensional transverse magnetic time harmonic Maxwell’s equations with general material properties and general boundary conditions. Zbl 1373.78416Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 19 2016 A \(C^0\) interior penalty method for elliptic distributed optimal control problems in three dimensions with pointwise state constraints. Zbl 1384.65038Brenner, Susanne C.; Oh, Minah; Pollock, Sara; Porwal, Kamana; Schedensack, Mira; Sharma, Natasha S. 11 2016 Topics in numerical partial differential equations and scientific computing. Based on the presentations at the 2nd IMA’s Women in Applied Mathematics, WhAM!, research collaboration workshop, Minneapolis, MN, USA, August 12–15, 2014. Zbl 1353.65001 1 2016 Forty years of the Crouzeix-Raviart element. Zbl 1310.65142Brenner, Susanne C. 28 2015 \(C^0\) Interior penalty Galerkin method for biharmonic eigenvalue problems. Zbl 1349.65439Brenner, Susanne C.; Monk, Peter; Sun, Jiguang 25 2015 Post-processing procedures for an elliptic distributed optimal control problem with pointwise state constraints. Zbl 1320.65169Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Yi 7 2015 A partition of unity method for the obstacle problem of simply supported Kirchhoff plates. Zbl 1342.74177Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng 2 2015 Piecewise \(\mathrm{H}^1\) functions and vector fields associated with meshes generated by independent refinements. Zbl 1311.65143Brenner, Susanne C.; Sung, Li-Yeng 1 2015 A quadratic \(C^0\) interior penalty method for an elliptic optimal control problem with state constraints. Zbl 1282.65074Brenner, S. C.; Sung, L.-Y.; Zhang, Y. 17 2014 A partition of unity method for a class of fourth order elliptic variational inequalities. Zbl 1425.65070Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng 16 2014 Multigrid methods for saddle point problems: Stokes and Lamé systems. Zbl 1298.76067Brenner, Susanne C.; Li, Hengguang; Sung, Li-Yeng 10 2014 A partition of unity method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1293.74424Brenner, Susanne C.; Davis, Christopher B.; Sung, Li-yeng 7 2014 A mixed finite element method for the Stokes equations based on a weakly over-penalized symmetric interior penalty approach. Zbl 1306.65276Barker, Andrew T.; Brenner, Susanne C. 6 2014 A one-level additive Schwarz preconditioner for a discontinuous Petrov-Galerkin method. Zbl 1382.65432Barker, Andrew T.; Brenner, Susanne C.; Park, Eun-Hee; Sung, Li-Yeng 4 2014 A Morley finite element method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1290.65108Brenner, Susanne C.; Sung, Li-yeng; Zhang, Hongchao; Zhang, Yi 29 2013 Isoparametric \(C ^{0}\) interior penalty methods for plate bending problems on smooth domains. Zbl 1341.74147Brenner, Susanne C.; Neilan, Michael; Sung, Li-Yeng 11 2013 A balancing domain decomposition by constraints preconditioner for a weakly over-penalized symmetric interior penalty method. Zbl 1313.65049Brenner, Susanne C.; Park, Eun-Hee; Sung, Li-Yeng 10 2013 An adaptive \(P_1\) finite element method for two-dimensional Maxwell’s equations. Zbl 1266.78027Brenner, S. C.; Gedicke, J.; Sung, L.-Y. 7 2013 An additive analysis of multiplicative Schwarz methods. Zbl 1271.65147Brenner, Susanne C. 3 2013 A quadratic \(C^0\) interior penalty method for the displacement obstacle problem of clamped Kirchhoff plates. Zbl 1263.65110Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Hongchao; Zhang, Yi 32 2012 Finite element methods for the displacement obstacle problem of clamped plates. Zbl 1250.74023Brenner, Susanne C.; Sung, Li-Yeng; Zhang, Yi 27 2012 \(C^{0}\) interior penalty methods. Zbl 1248.65120Brenner, Susanne C. 27 2012 Finite element approximations of the three dimensional Monge-Ampère equation. Zbl 1272.65088Brenner, Susanne Cecelia; Neilan, Michael 19 2012 Hodge decomposition for divergence-free vector fields and two-dimensional Maxwell’s equations. Zbl 1274.78089Brenner, S. C.; Cui, J.; Nan, Z.; Sung, L.-Y. 19 2012 A quadratic \(C^0\) interior penalty method for linear fourth order boundary value problems with boundary conditions of the Cahn-Hilliard type. Zbl 1256.65101Brenner, Susanne C.; Gu, Shiyuan; Gudi, Thirupathi; Sung, Li-Yeng 15 2012 Higher order weakly over-penalized symmetric interior penalty methods. Zbl 1273.65174Brenner, Susanne C.; Owens, Luke; Sung, Li-Yeng 13 2012 Schwarz methods for a preconditioned WOPSIP method for elliptic problems. Zbl 1284.65162Antonietti, Paola F.; Ayuso de Dios, Blanca; Brenner, Susanne C.; Sung, Li-yeng 12 2012 An iterative substructuring algorithm for a \(C^{0}\) interior penalty method. Zbl 1321.65181Brenner, Susanne C.; Wang, Kening 3 2012 \(\mathcal{C}^{0}\) penalty methods for the fully nonlinear Monge-Ampère equation. Zbl 1228.65220Brenner, Susanne C.; Gudi, Thirupathi; Neilan, Michael; Sung, Li-Yeng 48 2011 A \(\mathcal C^0\) interior penalty method for a fourth order elliptic singular perturbation problem. Zbl 1225.65108Brenner, Susanne C.; Neilan, Michael 29 2011 Multigrid algorithms for symmetric discontinuous Galerkin methods on graded meshes. Zbl 1229.65224Brenner, S. C.; Cui, J.; Gudi, T.; Sung, L.-Y. 15 2011 Two-level additive Schwarz preconditioners for a weakly over-penalized symmetric interior penalty method. Zbl 1230.65124Barker, A. T.; Brenner, S. C.; Park, E.-H.; Sung, L.-Y. 12 2011 Overlapping Schwarz domain decomposition preconditioners for the local discontinuous Galerkin method for elliptic problems. Zbl 1232.65164Barker, A. T.; Brenner, S. C.; Sung, L.-Y. 7 2011 An a posteriori error estimator for a quadratic \(C^{0}\)-interior penalty method for the biharmonic problem. Zbl 1201.65197Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 40 2010 A weakly over-penalized symmetric interior penalty method for the biharmonic problem. Zbl 1205.65311Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 14 2010 An intrinsically parallel finite element method. Zbl 1203.65244Brenner, S. C.; Gudi, T.; Owens, L.; Sung, L.-Y. 12 2010 Multigrid methods for the symmetric interior penalty method on graded meshes. Zbl 1224.65288Brenner, S. C.; Cui, J.; Sung, L.-Y. 23 2009 A posteriori error control for a weakly over-penalized symmetric interior penalty method. Zbl 1203.65230Brenner, Susanne C.; Gudi, Thirupathi; Sung, Li-Yeng 12 2009 A nonconforming penalty method for a two-dimensional curl-curl problem. Zbl 1168.78315Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 10 2009 Nonconforming Maxwell eigensolvers. Zbl 1203.65236Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 9 2009 A quadratic nonconforming vector finite element for \(H(\text{curl}; \varOmega)\cap H(\text{div}; \varOmega)\). Zbl 1170.65091Brenner, Susanne C.; Sung, Li-Yeng 4 2009 The mathematical theory of finite element methods. 3rd ed. Zbl 1135.65042Brenner, Susanne C.; Scott, L. Ridgway 1,266 2008 A weakly over-penalized symmetric interior penalty method. Zbl 1171.65077Brenner, Susanne C.; Owens, Luke; Sung, Li-Yeng 44 2008 A locally divergence-free interior penalty method for two-dimensional curl-curl problems. Zbl 1168.65068Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 35 2008 A nonconforming finite element method for a two-dimensional curl-curl and grad-div problem. Zbl 1166.78006Brenner, S. C.; Cui, J.; Li, F.; Sung, L.-Y. 25 2008 BDDC and FETI-DP without matrices or vectors. Zbl 1173.65363Brenner, Susanne C.; Sung, Li-Yeng 47 2007 A locally divergence-free nonconforming finite element method for the time-harmonic Maxwell equations. Zbl 1126.78017Brenner, Susanne C.; Li, Fengyan; Sung, Li-Yeng 32 2007 A \(W\)-cycle algorithm for a weakly over-penalized interior penalty method. Zbl 1173.65368Brenner, Susanne C.; Owens, Luke 15 2007 A weakly over-penalized non-symmetric interior penalty method. Zbl 1145.65095Brenner, Susanne C.; Owens, Luke 14 2007 Multigrid algorithms for \(C^0\) interior penalty methods. Zbl 1114.65151Brenner, Susanne C.; Sung, Li-yeng 14 2006 \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains. Zbl 1071.65151Brenner, Susanne C.; Sung, Li-Yeng 157 2005 Convergence of multigrid algorithms for interior penalty methods. Zbl 1073.65117Brenner, Susanne C.; Zhao, Jie 30 2005 Two-level additive Schwarz preconditioners for \(C^0\) interior penalty methods. Zbl 1088.65108Brenner, Susanne C.; Wang, Kening 16 2005 Korn’s inequalities for piecewise \(H^1\) vector fields. Zbl 1055.65118Brenner, Susanne C. 147 2004 Poincaré–Friedrichs inequalities for piecewise \(H^2\) functions. Zbl 1072.65147Brenner, Susanne C.; Wang, Kening; Zhao, Jie 30 2004 Convergence of nonconforming \(V\)-cycle and \(F\)-cycle multigrid algorithms for second order elliptic boundary value problems. Zbl 1052.65102Brenner, Susanne C. 18 2004 Discrete Sobolev and Poincaré inequalities for piecewise polynomial functions. Zbl 1065.65128Brenner, Susanne C. 9 2004 Poincaré–Friedrichs inequalities for piecewise \(H^{1}\) functions. Zbl 1045.65100Brenner, Susanne C. 225 2003 Analysis of two-dimensional FETI-DP preconditioners by the standard additive Schwarz framework. Zbl 1065.65136Brenner, Susanne 8 2003 Multigrid methods for the computation of singular solutions and stress intensity factors. III: Interface singularities. Zbl 1054.74047Brenner, Susanne C.; Sung, Li-yeng 4 2003 Lower bounds for three-dimensional nonoverlapping domain decomposition algorithms. Zbl 1054.65043Brenner, Susanne C.; He, Qingmi 3 2003 An additive Schwarz preconditioner for the FETI method. Zbl 1030.65115Brenner, Susanne C. 3 2003 The mathematical theory of finite element methods. 2nd ed. Zbl 1012.65115Brenner, Susanne C.; Scott, L. Ridgway 455 2002 Convergence of the multigrid \(V\)-cycle algorithm for second-order boundary value problems without full elliptic regularity. Zbl 0990.65121Brenner, Susanne C. 19 2002 Smoothers, mesh dependent norms, interpolation and multigrid. Zbl 1022.65134Brenner, Susanne C. 3 2002 A new look at FETI. Zbl 1026.65096Brenner, Susanne C. 1 2002 Some nonstandard finite element estimates with applications to \(3D\) Poisson and Signorini problems. Zbl 0981.65131Ben Belgacem, Faker; Brenner, Susanne C. 11 2001 Long-range correlations and trends in global climate models: Comparison with real data. Zbl 0978.86005Govindan, R. B.; Vjushin, D.; Brenner, S.; Bunde, A.; Havlin, S.; Schellnhuber, H.-J. 2 2001 Lower bounds for two-level additive Schwarz preconditioners with small overlap. Zbl 0959.65062Brenner, Susanne C. 6 2000 ...and 26 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 3,569 Authors 84 Brenner, Susanne Cecelia 72 Carstensen, Carsten 43 Huang, Jianguo 42 Huang, Yunqing 38 Zhang, Shangyou 37 Beirão da Veiga, Lourenço 33 Li, Jichun 33 Zhang, Zhimin 32 Gudi, Thirupathi 31 Han, Weimin 31 Yang, Yidu 30 Chen, Shaochun 29 Larson, Mats G. 28 Neilan, Michael 27 Antonietti, Paola Francesca 27 Huang, Xuehai 26 Nataraj, Neela 26 Rebholz, Leo G. 25 Feng, Xiaobing 25 Girault, Vivette 25 Ye, Xiu 24 Bi, Hai 24 Manzini, Gianmarco 24 Nochetto, Ricardo Horacio 23 Li, Hengguang 23 Xie, Hehu 22 He, Yinnian 22 Lamichhane, Bishnu Prasad 21 Pani, Amiya Kumar 21 Shi, Zhongci 20 Bartels, Sören 20 Hansbo, Peter 20 Mao, Shipeng 20 Mora, David 20 Shi, Dongyang 19 Chen, Long 19 Vabishchevich, Pëtr Nikolaevich 19 Vacca, Giuseppe 18 Badia, Santiago 18 Chen, Jinru 18 Di Pietro, Daniele Antonio 18 Gedicke, Joscha 18 Hu, Jun 18 Scott, Larkin Ridgway 18 Xu, Xuejun 17 Burman, Erik 17 Chung, Tsz Shun Eric 17 Gatica, Gabriel N. 17 Peterseim, Daniel 17 Xu, Jinchao 17 Yang, Suh-Yuh 16 Bacuta, Constantin 16 Cockburn, Bernardo 16 Ern, Alexandre 16 Guo, Hailong 16 Wohlmuth, Barbara I. 16 Zhao, Jikun 15 Casas, Eduardo 15 Dassi, Franco 15 Kwak, Do Young 15 Mu, Lin 15 Park, Eun-Jae 15 Wu, Haijun 14 Codina, Ramon 14 Duan, Huoyuan 14 Hiptmair, Ralf 14 Huang, Qiumei 14 Marcinkowski, Leszek 14 Verani, Marco 14 Wheeler, Mary Fanett 14 Yang, Wei 13 Chen, Yanping 13 Cui, Jintao 13 Droniou, Jérôme 13 Han, Jiayu 13 Makridakis, Charalambos G. 13 Prohl, Andreas 13 Rivière, Beatrice M. 13 Wollner, Winnifried 13 Yang, Min 12 Bi, Chunjia 12 Guan, Hongbo 12 Hinze, Michael 12 Kim, Hyea Hyun 12 Liu, Jiangguo 12 Mascotto, Lorenzo 12 Monk, Peter B. 12 Porwal, Kamana 12 Qiu, Weifeng 12 Schwab, Christoph 12 Sinha, Rajen Kumar 12 Tsuchiya, Takuya 12 Wang, Fei 12 Wang, Junping 12 Zhang, Shuo 12 Zikatanov, Ludmil T. 11 An, Rong 11 Brezzi, Franco 11 Chen, Zhangxin 11 Gunzburger, Max D. ...and 3,469 more Authors all top 5 Cited in 261 Serials 283 Journal of Scientific Computing 278 Computer Methods in Applied Mechanics and Engineering 253 Mathematics of Computation 227 Journal of Computational and Applied Mathematics 227 Numerische Mathematik 196 Computers & Mathematics with Applications 145 SIAM Journal on Numerical Analysis 127 Applied Numerical Mathematics 110 Journal of Computational Physics 110 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 97 Applied Mathematics and Computation 94 Numerical Methods for Partial Differential Equations 91 SIAM Journal on Scientific Computing 65 Advances in Computational Mathematics 62 Computational Methods in Applied Mathematics 57 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 46 Calcolo 35 Journal of Mathematical Analysis and Applications 32 BIT 28 Journal of Numerical Mathematics 27 International Journal for Numerical Methods in Engineering 27 Numerical Functional Analysis and Optimization 25 Japan Journal of Industrial and Applied Mathematics 25 Numerical Algorithms 24 Applied Mathematics Letters 22 Computational Optimization and Applications 21 International Journal of Computer Mathematics 21 Science China. Mathematics 20 Mathematical Methods in the Applied Sciences 19 Computational Geosciences 18 Advances in Applied Mathematics and Mechanics 17 Applications of Mathematics 17 Numerical Linear Algebra with Applications 17 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 17 Communications in Computational Physics 14 Multiscale Modeling & Simulation 14 International Journal of Numerical Analysis and Modeling 13 Communications in Numerical Methods in Engineering 12 Computers and Fluids 12 Computing 12 Discrete and Continuous Dynamical Systems. Series B 11 Engineering Analysis with Boundary Elements 11 Mathematical Problems in Engineering 10 Mathematics and Computers in Simulation 10 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 10 Foundations of Computational Mathematics 10 Comptes Rendus. Mathématique. Académie des Sciences, Paris 10 East Asian Journal on Applied Mathematics 9 Science in China. Series A 9 Applied Mathematical Modelling 9 Computational and Applied Mathematics 9 Results in Applied Mathematics 8 Applicable Analysis 8 SIAM Journal on Control and Optimization 8 Computational Mechanics 8 Electronic Research Archive 7 Journal of Approximation Theory 7 Applied Mathematics and Mechanics. (English Edition) 7 Journal of Computational Mathematics 7 ETNA. Electronic Transactions on Numerical Analysis 7 Discrete and Continuous Dynamical Systems. Series S 7 Mathematical Control and Related Fields 6 Abstract and Applied Analysis 6 Communications on Pure and Applied Analysis 6 Journal of Applied Mathematics and Computing 6 International Journal of Computational Methods 6 SIAM/ASA Journal on Uncertainty Quantification 6 Communications on Applied Mathematics and Computation 5 Archive for Rational Mechanics and Analysis 5 Journal of Optimization Theory and Applications 5 Acta Applicandae Mathematicae 5 Journal of Integral Equations and Applications 5 Computational Mathematics and Mathematical Physics 5 Applied Mathematics. Series B (English Edition) 5 Communications in Nonlinear Science and Numerical Simulation 5 Central European Journal of Mathematics 5 Analysis and Applications (Singapore) 4 International Journal for Numerical Methods in Fluids 4 Journal of the Mechanics and Physics of Solids 4 Applied Mathematics and Optimization 4 RAIRO. Modélisation Mathématique et Analyse Numérique 4 Journal of Complexity 4 Journal of Nonlinear Science 4 Journal of Inverse and Ill-Posed Problems 4 Russian Journal of Numerical Analysis and Mathematical Modelling 4 Mathematics and Mechanics of Solids 4 Computing and Visualization in Science 4 Optimization Methods & Software 4 Journal of Mathematical Fluid Mechanics 4 Archives of Computational Methods in Engineering 4 Journal of Applied Mathematics 4 Advances in Numerical Analysis 4 SMAI Journal of Computational Mathematics 3 Indian Journal of Pure & Applied Mathematics 3 Inverse Problems 3 Meccanica 3 Computer Aided Geometric Design 3 Acta Mathematicae Applicatae Sinica. English Series 3 Mathematical and Computer Modelling 3 SIAM Journal on Matrix Analysis and Applications ...and 161 more Serials all top 5 Cited in 46 Fields 3,152 Numerical analysis (65-XX) 1,704 Partial differential equations (35-XX) 791 Fluid mechanics (76-XX) 641 Mechanics of deformable solids (74-XX) 240 Calculus of variations and optimal control; optimization (49-XX) 183 Optics, electromagnetic theory (78-XX) 75 Approximations and expansions (41-XX) 68 Probability theory and stochastic processes (60-XX) 56 Biology and other natural sciences (92-XX) 52 Statistical mechanics, structure of matter (82-XX) 49 Functional analysis (46-XX) 41 Potential theory (31-XX) 39 Real functions (26-XX) 36 Operator theory (47-XX) 33 Geophysics (86-XX) 31 Ordinary differential equations (34-XX) 30 Computer science (68-XX) 30 Operations research, mathematical programming (90-XX) 27 Integral equations (45-XX) 24 Global analysis, analysis on manifolds (58-XX) 24 Systems theory; control (93-XX) 23 Classical thermodynamics, heat transfer (80-XX) 21 Linear and multilinear algebra; matrix theory (15-XX) 17 Statistics (62-XX) 16 Quantum theory (81-XX) 15 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 11 Harmonic analysis on Euclidean spaces (42-XX) 9 Dynamical systems and ergodic theory (37-XX) 9 Information and communication theory, circuits (94-XX) 8 Special functions (33-XX) 8 Differential geometry (53-XX) 7 Mechanics of particles and systems (70-XX) 4 General and overarching topics; collections (00-XX) 4 Combinatorics (05-XX) 4 Astronomy and astrophysics (85-XX) 3 History and biography (01-XX) 3 Mathematical logic and foundations (03-XX) 3 Measure and integration (28-XX) 2 Difference and functional equations (39-XX) 2 Convex and discrete geometry (52-XX) 2 Relativity and gravitational theory (83-XX) 1 Category theory; homological algebra (18-XX) 1 Functions of a complex variable (30-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-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.