Edit Profile (opens in new tab) Arnold, Douglas Norman Co-Author Distance Author ID: arnold.douglas-n Published as: Arnold, Douglas N.; Arnold, D. N.; Arnold, Douglas more...less Homepage: http://www-users.math.umn.edu/~arnold/ External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef Documents Indexed: 91 Publications since 1979, including 1 Book and 1 Additional arXiv Preprint 3 Contributions as Editor Co-Authors: 55 Co-Authors with 80 Joint Publications 1,687 Co-Co-Authors all top 5 Co-Authors 14 single-authored 24 Falk, Richard S. 16 Winther, Ragnar 9 Brezzi, Franco 6 Awanou, Gerard Michel 4 Boffi, Daniele 4 Douglas, Jim jun. 4 Filoche, Marcel 4 Madureira, Alexandre L. 4 Marini, Luisa Donatella 4 Mayboroda, Svitlana 3 David, Guy 3 Fowler, Kristine K. 3 Mukherjee, Arup 3 Wendland, Wolfgang L. 2 Babuška, Ivo 2 Cockburn, Bernardo 2 Guzmán, Johnny 2 Jerison, David S. 2 Liu, Xiaobo 2 Osborn, John E. 2 Pouly, Luc 2 Wang, Wei 2 Zhang, Shiwen 1 Alessandrini, Stephan M. 1 Alessandrini, Stephen M. 1 Alonso Rodríguez, Ana 1 Bochev, Pavel B. 1 Bonizzoni, Francesca 1 Chen, Hongtao 1 Cheng, R. S.-C. 1 Desforges, Perceval 1 Fortin, Michel 1 Gastaldi, Lucia 1 Gopalakrishnan, Jay 1 Gupta, Chaitan P. 1 Hu, Kaibo 1 Lee, Jeonghun J. 1 Lehoucq, Richard B. 1 Li, Lizao 1 Nicolaides, Roy A. 1 Noon, Patrick J. 1 Pauly, Dirk 1 Qiu, Weifeng 1 Rapetti, Francesca 1 Rognes, Marie Elisabeth 1 Rogness, Jonathan 1 Saranen, Jukka 1 Scott, Larkin Ridgway 1 Shashkov, Mikhail J. 1 Tarfulea, Nicolae 1 Thomée, Vidar 1 Tsogtgerel, Gantumur 1 Vogelius, Michael S. 1 Walker, Shawn W. 1 Zhang, Sheng all top 5 Serials 11 Mathematics of Computation 7 Numerische Mathematik 7 SIAM Journal on Numerical Analysis 6 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 4 Computer Methods in Applied Mechanics and Engineering 3 Calcolo 3 RAIRO. Modélisation Mathématique et Analyse Numérique 3 Notices of the American Mathematical Society 2 SIAM Journal on Mathematical Analysis 2 SIAM Journal on Scientific Computing 2 Advances in Computational Mathematics 2 La Gaceta de la Real Sociedad Matemática Española 2 Foundations of Computational Mathematics 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Archive for Rational Mechanics and Analysis 1 Communications in Mathematical Physics 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 1 The Australian Mathematical Society Gazette 1 Transactions of the American Mathematical Society 1 Rendiconti. Scienze Matemàtiche e Applicazioni. A 1 Journal of Computational Mathematics 1 Japan Journal of Applied Mathematics 1 Journal of Scientific Computing 1 Journal of Integral Equations and Applications 1 Communications in Partial Differential Equations 1 Journal of Elasticity 1 Bulletin of the American Mathematical Society. New Series 1 Matemática Aplicada e Computacional 1 Communications in Numerical Methods in Engineering 1 Electronic Journal of Differential Equations (EJDE) 1 Computational and Applied Mathematics 1 European Mathematical Society Newsletter 1 Acta Numerica 1 Oberwolfach Reports 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 The IMA Volumes in Mathematics and its Applications 1 Acta Numerica all top 5 Fields 62 Numerical analysis (65-XX) 45 Partial differential equations (35-XX) 38 Mechanics of deformable solids (74-XX) 12 Global analysis, analysis on manifolds (58-XX) 5 General and overarching topics; collections (00-XX) 5 Integral equations (45-XX) 5 Fluid mechanics (76-XX) 4 History and biography (01-XX) 3 Operator theory (47-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Relativity and gravitational theory (83-XX) 2 Ordinary differential equations (34-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Quantum theory (81-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Difference and functional equations (39-XX) 1 Approximations and expansions (41-XX) 1 Manifolds and cell complexes (57-XX) 1 Probability theory and stochastic processes (60-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 83 Publications have been cited 6,732 times in 4,311 Documents Cited by ▼ Year ▼ Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella 1,389 2002 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 725 1982 A stable finite element for the Stokes equations. Zbl 0593.76039 Arnold, D. N.; Brezzi, F.; Fortin, M. 461 1984 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 420 2006 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078 Arnold, D. N.; Brezzi, F. 369 1985 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 257 2010 Mixed finite elements for elasticity. Zbl 1090.74051 Arnold, Douglas N.; Winther, Ragnar 211 2002 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074 Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 200 1984 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 157 2007 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040 Arnold, Douglas N.; Falk, Richard S. 142 1989 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066 Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 139 1984 Multigrid in H(div) and H(curl). Zbl 0974.65113 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 114 2000 Approximation by quadrilateral finite elements. Zbl 0993.65125 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 113 2002 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 109 2008 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 108 2005 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112 Arnold, Douglas N.; Falk, Richard S.; Winther, R. 92 1997 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066 Arnold, Douglas N. 82 1981 Finite element exterior calculus. Zbl 1506.65001 Arnold, Douglas N. 75 2018 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 73 2000 On the asymptotic convergence of collocation methods. Zbl 0541.65075 Arnold, Douglas N.; Wendland, Wolfgang L. 70 1983 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077 Arnold, Douglas N.; Wendland, Wolfgang L. 67 1985 The serendipity family of finite elements. Zbl 1218.65125 Arnold, Douglas N.; Awanou, Gerard 63 2011 Mixed finite element methods for elliptic problems. Zbl 0729.73198 Arnold, Douglas N. 60 1990 Nonconforming mixed elements for elasticity. Zbl 1057.74036 Arnold, Douglas N.; Winther, Ragnar 57 2003 Rectangular mixed finite elements for elasticity. Zbl 1077.74044 Arnold, Douglas N.; Awanou, Gerard 55 2005 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116 Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 52 2000 A new mixed formulation for elasticity. Zbl 0621.73102 Arnold, Douglas N.; Falk, Richard S. 49 1988 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208 Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 48 1988 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042 Arnold, Douglas N.; Falk, Richard S. 46 1990 Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Zbl 0466.65062 Arnold, Douglas N.; Douglas, Jim jun.; Thomee, Vidar 45 1981 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 44 2009 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068 Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 41 2005 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027 Arnold, Douglas N.; Falk, Richard S. 40 1996 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 38 2006 Finite element differential forms on cubical meshes. Zbl 1297.65142 Arnold, Douglas N.; Awanou, Gerard 33 2014 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 30 2006 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087 Arnold, Douglas N. 29 1983 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117 Arnold, Douglas N.; Liu, Xiaobo 29 1995 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396 Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 29 2007 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193 Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 29 2015 Differential complexes and numerical stability. Zbl 1023.65113 Arnold, Douglas N. 29 2002 Locking-free finite element methods for shells. Zbl 0854.65095 Arnold, Douglas N.; Brezzi, Franco 28 1997 Localization of eigenfunctions via an effective potential. Zbl 1432.35061 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 26 2019 Coercivity of the single layer heat potential. Zbl 0672.65092 Arnold, Douglas N.; Noon, Patrick J. 24 1989 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058 Arnold, Douglas N.; Brezzi, Franco 24 1993 Computing spectra without solving eigenvalue problems. Zbl 1420.81009 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 24 2019 On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models. Zbl 1089.74595 Arnold, Douglas N.; Madureira, Alexandre L.; Zhang, Sheng 23 2002 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012 Arnold, Douglas N.; Falk, Richard S. 23 1987 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069 Arnold, Douglas N.; Saranen, Jukka 22 1984 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033 Arnold, Douglas N.; Lee, Jeonghun J. 21 2014 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 20 1997 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 19 2014 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100 Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 18 2012 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096 Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 18 2015 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068 Arnold, Douglas N.; Falk, Richard S. 17 1997 Spaces of finite element differential forms. Zbl 1290.58003 Arnold, Douglas N. 17 2013 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028 Arnold, Douglas N.; Winther, Ragnar 15 1982 Complexes from complexes. Zbl 1520.58011 Arnold, Douglas N.; Hu, Kaibo 15 2021 Derivation and justification of plate models by variational methods. Zbl 0958.74033 Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 14 1999 Compatible spatial discretizations. Papers presented at IMA hot topics workshop: compatible spatial discretizations for partial differential equations, Minneapolis, MN, USA, May 11–15, 2004. Zbl 1097.65003 14 2006 Finite element approximation on quadrilateral meshes. Zbl 0999.76073 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 Möbius transformations revealed. Zbl 1200.30036 Arnold, Douglas N.; Rogness, Jonathan 10 2008 Innovative finite element methods for plates. Zbl 0757.73048 Arnold, Douglas N. 10 1991 Finite element methods: Principles for their selection. Zbl 0513.73081 Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078 Arnold, D. N.; Falk, R. S.; Winther, R. 9 1998 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388 Arnold, Douglas N.; Winther, Ragnar 8 2003 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128 Arnold, Douglas N. 8 1994 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182 Arnold, Douglas N.; Walker, Shawn W. 8 2020 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094 Arnold, D. N.; Douglas, Jim jun. 7 1979 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092 Arnold, D. N.; Wendland, W. L. 6 1982 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067 Cheng, R. S.-C.; Arnold, D. N. 6 1988 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585 Arnold, Douglas N.; Liu, Xiaobo 6 1997 Asymptotic estimates of hierarchical modeling. Zbl 1046.35024 Arnold, Douglas N.; Madureira, Alexandre L. 5 2003 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132 Arnold, Douglas N.; Rognes, Marie E. 4 2009 Finite element exterior calculus for parabolic problems. Zbl 1362.65100 Arnold, Douglas N.; Chen, Hongtao 4 2017 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175 Arnold, Douglas; Guzmán, Johnny 4 2021 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134 Arnold, Douglas N.; Tarfulea, Nicolae 3 2007 Finite element exterior calculus with lower-order terms. Zbl 1364.65236 Arnold, Douglas N.; Li, Lizao 3 2017 On the consistency of the combinatorial codifferential. Zbl 1298.58003 Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 Nefarious numbers. Zbl 1223.01042 Arnold, Douglas N.; Fowler, Kristine K. 2 2011 The landscape law for tight binding Hamiltonians. Zbl 1511.35109 Arnold, Douglas; Filoche, Marcel; Mayboroda, Svitlana; Wang, Wei; Zhang, Shiwen 2 2022 Adaptive finite elements and colliding black holes. Zbl 0902.65080 Arnold, D. N.; Mukherjee, A.; Pouly, L. 1 1998 Numerical problems in general relativity. Zbl 0976.83002 Arnold, Douglas N. 1 2000 The landscape law for tight binding Hamiltonians. Zbl 1511.35109 Arnold, Douglas; Filoche, Marcel; Mayboroda, Svitlana; Wang, Wei; Zhang, Shiwen 2 2022 Complexes from complexes. Zbl 1520.58011 Arnold, Douglas N.; Hu, Kaibo 15 2021 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175 Arnold, Douglas; Guzmán, Johnny 4 2021 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182 Arnold, Douglas N.; Walker, Shawn W. 8 2020 Localization of eigenfunctions via an effective potential. Zbl 1432.35061 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 26 2019 Computing spectra without solving eigenvalue problems. Zbl 1420.81009 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 24 2019 Finite element exterior calculus. Zbl 1506.65001 Arnold, Douglas N. 75 2018 Finite element exterior calculus for parabolic problems. Zbl 1362.65100 Arnold, Douglas N.; Chen, Hongtao 4 2017 Finite element exterior calculus with lower-order terms. Zbl 1364.65236 Arnold, Douglas N.; Li, Lizao 3 2017 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193 Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 29 2015 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096 Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 18 2015 Finite element differential forms on cubical meshes. Zbl 1297.65142 Arnold, Douglas N.; Awanou, Gerard 33 2014 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033 Arnold, Douglas N.; Lee, Jeonghun J. 21 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 19 2014 On the consistency of the combinatorial codifferential. Zbl 1298.58003 Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 Spaces of finite element differential forms. Zbl 1290.58003 Arnold, Douglas N. 17 2013 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100 Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 18 2012 The serendipity family of finite elements. Zbl 1218.65125 Arnold, Douglas N.; Awanou, Gerard 63 2011 Nefarious numbers. Zbl 1223.01042 Arnold, Douglas N.; Fowler, Kristine K. 2 2011 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 257 2010 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 44 2009 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132 Arnold, Douglas N.; Rognes, Marie E. 4 2009 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 109 2008 Möbius transformations revealed. Zbl 1200.30036 Arnold, Douglas N.; Rogness, Jonathan 10 2008 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 157 2007 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396 Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 29 2007 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134 Arnold, Douglas N.; Tarfulea, Nicolae 3 2007 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 420 2006 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 38 2006 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 30 2006 Compatible spatial discretizations. Papers presented at IMA hot topics workshop: compatible spatial discretizations for partial differential equations, Minneapolis, MN, USA, May 11–15, 2004. Zbl 1097.65003 14 2006 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 108 2005 Rectangular mixed finite elements for elasticity. Zbl 1077.74044 Arnold, Douglas N.; Awanou, Gerard 55 2005 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068 Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 41 2005 Nonconforming mixed elements for elasticity. Zbl 1057.74036 Arnold, Douglas N.; Winther, Ragnar 57 2003 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388 Arnold, Douglas N.; Winther, Ragnar 8 2003 Asymptotic estimates of hierarchical modeling. Zbl 1046.35024 Arnold, Douglas N.; Madureira, Alexandre L. 5 2003 Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella 1,389 2002 Mixed finite elements for elasticity. Zbl 1090.74051 Arnold, Douglas N.; Winther, Ragnar 211 2002 Approximation by quadrilateral finite elements. Zbl 0993.65125 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 113 2002 Differential complexes and numerical stability. Zbl 1023.65113 Arnold, Douglas N. 29 2002 On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models. Zbl 1089.74595 Arnold, Douglas N.; Madureira, Alexandre L.; Zhang, Sheng 23 2002 Finite element approximation on quadrilateral meshes. Zbl 0999.76073 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 Multigrid in H(div) and H(curl). Zbl 0974.65113 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 114 2000 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 73 2000 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116 Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 52 2000 Numerical problems in general relativity. Zbl 0976.83002 Arnold, Douglas N. 1 2000 Derivation and justification of plate models by variational methods. Zbl 0958.74033 Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 14 1999 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078 Arnold, D. N.; Falk, R. S.; Winther, R. 9 1998 Adaptive finite elements and colliding black holes. Zbl 0902.65080 Arnold, D. N.; Mukherjee, A.; Pouly, L. 1 1998 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112 Arnold, Douglas N.; Falk, Richard S.; Winther, R. 92 1997 Locking-free finite element methods for shells. Zbl 0854.65095 Arnold, Douglas N.; Brezzi, Franco 28 1997 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 20 1997 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068 Arnold, Douglas N.; Falk, Richard S. 17 1997 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585 Arnold, Douglas N.; Liu, Xiaobo 6 1997 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027 Arnold, Douglas N.; Falk, Richard S. 40 1996 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117 Arnold, Douglas N.; Liu, Xiaobo 29 1995 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128 Arnold, Douglas N. 8 1994 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058 Arnold, Douglas N.; Brezzi, Franco 24 1993 Innovative finite element methods for plates. Zbl 0757.73048 Arnold, Douglas N. 10 1991 Mixed finite element methods for elliptic problems. Zbl 0729.73198 Arnold, Douglas N. 60 1990 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042 Arnold, Douglas N.; Falk, Richard S. 46 1990 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040 Arnold, Douglas N.; Falk, Richard S. 142 1989 Coercivity of the single layer heat potential. Zbl 0672.65092 Arnold, Douglas N.; Noon, Patrick J. 24 1989 A new mixed formulation for elasticity. Zbl 0621.73102 Arnold, Douglas N.; Falk, Richard S. 49 1988 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208 Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 48 1988 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067 Cheng, R. S.-C.; Arnold, D. N. 6 1988 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012 Arnold, Douglas N.; Falk, Richard S. 23 1987 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078 Arnold, D. N.; Brezzi, F. 369 1985 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077 Arnold, Douglas N.; Wendland, Wolfgang L. 67 1985 A stable finite element for the Stokes equations. Zbl 0593.76039 Arnold, D. N.; Brezzi, F.; Fortin, M. 461 1984 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074 Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 200 1984 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066 Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 139 1984 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069 Arnold, Douglas N.; Saranen, Jukka 22 1984 Finite element methods: Principles for their selection. Zbl 0513.73081 Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 On the asymptotic convergence of collocation methods. Zbl 0541.65075 Arnold, Douglas N.; Wendland, Wolfgang L. 70 1983 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087 Arnold, Douglas N. 29 1983 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 725 1982 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028 Arnold, Douglas N.; Winther, Ragnar 15 1982 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092 Arnold, D. N.; Wendland, W. L. 6 1982 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066 Arnold, Douglas N. 82 1981 Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Zbl 0466.65062 Arnold, Douglas N.; Douglas, Jim jun.; Thomee, Vidar 45 1981 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094 Arnold, D. N.; Douglas, Jim jun. 7 1979 all cited Publications top 5 cited Publications all top 5 Cited by 4,528 Authors 56 Cockburn, Bernardo 53 Gatica, Gabriel N. 42 Ye, Xiu 41 Zhang, Shangyou 40 Antonietti, Paola Francesca 35 Brezzi, Franco 34 Beirão da Veiga, Lourenço 33 Hughes, Thomas J. R. 31 Carstensen, Carsten 30 Arnold, Douglas Norman 30 Di Pietro, Daniele Antonio 30 Hu, Jun 30 Ruiz-Baier, Ricardo 30 Zhang, Zhimin 29 Sayas, Francisco-Javier 29 Schöberl, Joachim 29 Xu, Jinchao 28 Marini, Luisa Donatella 27 Bassi, Francesco 27 Huang, Xuehai 27 Schötzau, Dominik 26 Guzmán, Johnny 26 Hiptmair, Ralf 26 Lovadina, Carlo 26 Meddahi, Salim 26 Stenberg, Rolf 25 Chen, Zhangxin 25 Houston, Paul 25 Wheeler, Mary Fanett 25 Winther, Ragnar 24 Brenner, Susanne Cecelia 24 Chen, Long 24 He, Yinnian 23 Xie, Xiaoping 23 Yotov, Ivan 22 Franca, Leopoldo Luis Cabo Penna 22 Mu, Lin 22 Park, Eun-Jae 22 Rivière, Beatrice M. 21 Giani, Stefano 20 Huang, Yunqing 20 Wang, Junping 19 Pani, Amiya Kumar 19 Wang, Fei 18 Chen, Shaochun 18 Christiansen, Snorre Harald 18 Crivellini, Andrea 18 Ern, Alexandre 18 Evans, John A. 18 Gopalakrishnan, Jay 18 Hu, Kaibo 18 Marquez-Duran, Antonio M. 18 Neilan, Michael 18 Perugia, Ilaria 18 Scovazzi, Guglielmo 18 Vohralík, Martin 17 Bazilevs, Yuri 17 Gerritsma, Marc I. 17 Hu, Xiaozhe 17 Kanschat, Guido 17 Larson, Mats G. 17 Loula, Abimael Fernando Dourado 17 Nordström, Jan 17 Qiu, Weifeng 17 Shang, Yueqiang 17 Vassilevski, Panayot Spirov 16 Ainsworth, Mark 16 Boffi, Daniele 16 Gudi, Thirupathi 16 Kwak, Do Young 16 Lee, Jeonghun J. 16 Rapetti, Francesca 16 Russo, Alessandro 16 Wohlmuth, Barbara I. 16 Zikatanov, Ludmil T. 15 Botti, Lorenzo 15 Calo, Victor Manuel 15 Demkowicz, Leszek F. 15 Dolejší, Vít 15 Falk, Richard S. 15 Kraus, Johannes K. 15 Nguyen, Ngoc Cuong 15 Nordbotten, Jan Martin 15 Oyarzúa, Ricardo 15 Schwab, Christoph 15 Shi, Zhongci 15 Sung, Li-Yeng 14 Badia, Santiago 14 Buffa, Annalisa 14 Colombo, Alessandro G. 14 Duan, Huoyuan 14 Han, Weimin 14 Karasözen, Bülent 14 Reddy, B. Dayanand 14 Sacco, Riccardo 14 van der Vegt, Jaap J. W. 14 Wendland, Wolfgang L. 13 Barrios, Tomás P. 13 Bustinza, Rommel A. 13 Chen, Jinru ...and 4,428 more Authors all top 5 Cited in 278 Serials 537 Computer Methods in Applied Mechanics and Engineering 351 Journal of Computational Physics 282 Journal of Scientific Computing 210 Computers & Mathematics with Applications 199 Journal of Computational and Applied Mathematics 196 Numerische Mathematik 192 Mathematics of Computation 125 Applied Numerical Mathematics 119 SIAM Journal on Scientific Computing 109 SIAM Journal on Numerical Analysis 105 Numerical Methods for Partial Differential Equations 99 International Journal for Numerical Methods in Engineering 81 Computers and Fluids 78 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 75 Applied Mathematics and Computation 67 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 60 Computational Mechanics 53 Advances in Computational Mathematics 42 Calcolo 36 Computational Methods in Applied Mathematics 35 Computational Geosciences 31 Advances in Applied Mathematics and Mechanics 27 Numerical Algorithms 27 International Journal of Numerical Analysis and Modeling 26 International Journal for Numerical Methods in Fluids 26 RAIRO. Modélisation Mathématique et Analyse Numérique 25 Science China. Mathematics 23 Mathematics and Computers in Simulation 23 Journal of Numerical Mathematics 22 Journal of Mathematical Analysis and Applications 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 21 BIT 21 Applied Mathematics Letters 20 Foundations of Computational Mathematics 19 Applied Mathematical Modelling 19 Numerical Linear Algebra with Applications 19 Engineering Analysis with Boundary Elements 19 Communications in Computational Physics 18 Communications in Numerical Methods in Engineering 17 Journal of Integral Equations and Applications 17 Japan Journal of Industrial and Applied Mathematics 16 Applicable Analysis 16 Communications on Applied Mathematics and Computation 15 Mathematical Methods in the Applied Sciences 15 International Journal of Computer Mathematics 15 Computational and Applied Mathematics 15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 15 International Journal of Computational Methods 14 SMAI Journal of Computational Mathematics 13 Numerical Functional Analysis and Optimization 12 Computer Physics Communications 12 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 11 Applications of Mathematics 10 Computing 10 International Journal of Computational Fluid Dynamics 10 Archives of Computational Methods in Engineering 9 Acta Mechanica 9 Journal of Applied Mathematics and Computing 8 Integral Equations and Operator Theory 8 ETNA. Electronic Transactions on Numerical Analysis 8 Acta Numerica 7 Journal of Computational Mathematics 7 Mathematical Problems in Engineering 7 Computing and Visualization in Science 7 Abstract and Applied Analysis 7 European Journal of Mechanics. A. Solids 7 Discrete and Continuous Dynamical Systems. Series B 6 ACM Transactions on Mathematical Software 6 Journal of Elasticity 6 SIAM Review 6 Communications in Nonlinear Science and Numerical Simulation 6 Multiscale Modeling & Simulation 6 Oberwolfach Reports 6 Electronic Research Archive 5 Communications in Partial Differential Equations 5 Journal of Mathematical Sciences (New York) 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Journal of Applied Mathematics 5 Advances in Difference Equations 5 GEM - International Journal on Geomathematics 5 Journal of the Korean Society for Industrial and Applied Mathematics 5 East Asian Journal on Applied Mathematics 5 Results in Applied Mathematics 4 Archive for Rational Mechanics and Analysis 4 Journal of Mathematical Physics 4 ZAMP. Zeitschrift für angewandte Mathematik und Physik 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Applied Mathematics and Mechanics. (English Edition) 4 Computer Aided Geometric Design 4 Journal of Nonlinear Science 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Vietnam Journal of Mathematics 4 Engineering Computations 4 Boundary Value Problems 4 Discrete and Continuous Dynamical Systems. Series S 4 Advances in Mathematical Physics 4 S\(\vec{\text{e}}\)MA Journal 3 Inverse Problems 3 Journal of Engineering Mathematics 3 Journal of the Mechanics and Physics of Solids ...and 178 more Serials all top 5 Cited in 55 Fields 3,438 Numerical analysis (65-XX) 1,631 Partial differential equations (35-XX) 1,366 Fluid mechanics (76-XX) 1,050 Mechanics of deformable solids (74-XX) 209 Optics, electromagnetic theory (78-XX) 110 Global analysis, analysis on manifolds (58-XX) 106 Calculus of variations and optimal control; optimization (49-XX) 77 Geophysics (86-XX) 75 Integral equations (45-XX) 73 Statistical mechanics, structure of matter (82-XX) 56 Biology and other natural sciences (92-XX) 55 Classical thermodynamics, heat transfer (80-XX) 43 Approximations and expansions (41-XX) 41 Operator theory (47-XX) 34 Computer science (68-XX) 30 Potential theory (31-XX) 26 Differential geometry (53-XX) 25 Ordinary differential equations (34-XX) 23 Quantum theory (81-XX) 21 Functional analysis (46-XX) 19 Dynamical systems and ergodic theory (37-XX) 18 Probability theory and stochastic processes (60-XX) 14 Systems theory; control (93-XX) 13 Operations research, mathematical programming (90-XX) 12 Real functions (26-XX) 11 Mechanics of particles and systems (70-XX) 11 Relativity and gravitational theory (83-XX) 10 General and overarching topics; collections (00-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Combinatorics (05-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 Convex and discrete geometry (52-XX) 9 Statistics (62-XX) 8 Algebraic topology (55-XX) 8 Information and communication theory, circuits (94-XX) 7 Functions of a complex variable (30-XX) 6 Algebraic geometry (14-XX) 5 History and biography (01-XX) 5 Difference and functional equations (39-XX) 4 Special functions (33-XX) 4 Manifolds and cell complexes (57-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Measure and integration (28-XX) 3 Geometry (51-XX) 3 Astronomy and astrophysics (85-XX) 3 Mathematics education (97-XX) 2 Category theory; homological algebra (18-XX) 2 Integral transforms, operational calculus (44-XX) 1 Number theory (11-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Abstract harmonic analysis (43-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. 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