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: https://www-users.cse.umn.edu/~arnold/ External Links: MGP · ORCID · Wikidata · Google Scholar · 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 1,774 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 7,377 times in 4,712 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 1,517 2002 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060 Arnold, Douglas N. 782 1982 A stable finite element for the Stokes equations. Zbl 0593.76039 Arnold, D. N.; Brezzi, F.; Fortin, M. 505 1984 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 462 2006 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078 Arnold, D. N.; Brezzi, F. 404 1985 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 288 2010 Mixed finite elements for elasticity. Zbl 1090.74051 Arnold, Douglas N.; Winther, Ragnar 230 2002 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074 Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 204 1984 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 173 2007 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066 Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 146 1984 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040 Arnold, Douglas N.; Falk, Richard S. 144 1989 Multigrid in H(div) and H(curl). Zbl 0974.65113 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 134 2000 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 121 2008 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 120 2005 Approximation by quadrilateral finite elements. Zbl 0993.65125 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 117 2002 Finite element exterior calculus. Zbl 1506.65001 Arnold, Douglas N. 104 2018 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112 Arnold, Douglas N.; Falk, Richard S.; Winther, R. 103 1997 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 86 2000 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066 Arnold, Douglas N. 83 1981 On the asymptotic convergence of collocation methods. Zbl 0541.65075 Arnold, Douglas N.; Wendland, Wolfgang L. 73 1983 The serendipity family of finite elements. Zbl 1218.65125 Arnold, Douglas N.; Awanou, Gerard 70 2011 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077 Arnold, Douglas N.; Wendland, Wolfgang L. 67 1985 Mixed finite element methods for elliptic problems. Zbl 0729.73198 Arnold, Douglas N. 63 1990 Nonconforming mixed elements for elasticity. Zbl 1057.74036 Arnold, Douglas N.; Winther, Ragnar 63 2003 Rectangular mixed finite elements for elasticity. Zbl 1077.74044 Arnold, Douglas N.; Awanou, Gerard 58 2005 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208 Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 55 1988 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 55 2009 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116 Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 54 2000 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 52 1981 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042 Arnold, Douglas N.; Falk, Richard S. 47 1990 A new mixed formulation for elasticity. Zbl 0621.73102 Arnold, Douglas N.; Falk, Richard S. 45 1988 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068 Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 45 2005 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 42 2006 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. II: The elasticity complex. Zbl 1119.65399 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 40 2006 Localization of eigenfunctions via an effective potential. Zbl 1432.35061 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 38 2019 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193 Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 36 2015 Differential complexes and numerical stability. Zbl 1023.65113 Arnold, Douglas N. 35 2002 Finite element differential forms on cubical meshes. Zbl 1297.65142 Arnold, Douglas N.; Awanou, Gerard 35 2014 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117 Arnold, Douglas N.; Liu, Xiaobo 31 1995 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396 Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 30 2007 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087 Arnold, Douglas N. 29 1983 Computing spectra without solving eigenvalue problems. Zbl 1420.81009 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 29 2019 Locking-free finite element methods for shells. Zbl 0854.65095 Arnold, Douglas N.; Brezzi, Franco 27 1997 Complexes from complexes. Zbl 1520.58011 Arnold, Douglas N.; Hu, Kaibo 27 2021 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012 Arnold, Douglas N.; Falk, Richard S. 25 1987 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033 Arnold, Douglas N.; Lee, Jeonghun J. 25 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 25 2014 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058 Arnold, Douglas N.; Brezzi, Franco 24 1993 Coercivity of the single layer heat potential. Zbl 0672.65092 Arnold, Douglas N.; Noon, Patrick J. 24 1989 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 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 22 1997 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069 Arnold, Douglas N.; Saranen, Jukka 22 1984 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096 Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 21 2015 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 21 2006 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100 Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 20 2012 Spaces of finite element differential forms. Zbl 1290.58003 Arnold, Douglas N. 19 2013 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068 Arnold, Douglas N.; Falk, Richard S. 17 1997 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028 Arnold, Douglas N.; Winther, Ragnar 16 1982 Derivation and justification of plate models by variational methods. Zbl 0958.74033 Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 15 1999 Finite element approximation on quadrilateral meshes. Zbl 0999.76073 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078 Arnold, D. N.; Falk, R. S.; Winther, R. 12 1998 Innovative finite element methods for plates. Zbl 0757.73048 Arnold, Douglas N. 11 1991 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182 Arnold, Douglas N.; Walker, Shawn W. 11 2020 Möbius transformations revealed. Zbl 1200.30036 Arnold, Douglas N.; Rogness, Jonathan 10 2008 Finite element methods: Principles for their selection. Zbl 0513.73081 Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388 Arnold, Douglas N.; Winther, Ragnar 9 2003 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128 Arnold, Douglas N. 8 1994 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092 Arnold, D. N.; Wendland, W. L. 8 1982 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094 Arnold, D. N.; Douglas, Jim jun. 8 1979 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067 Cheng, R. S.-C.; Arnold, D. N. 7 1988 The landscape law for tight binding Hamiltonians. Zbl 1511.35109 Arnold, Douglas; Filoche, Marcel; Mayboroda, Svitlana; Wang, Wei; Zhang, Shiwen 6 2022 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175 Arnold, Douglas; Guzmán, Johnny 6 2021 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585 Arnold, Douglas N.; Liu, Xiaobo 5 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. 5 2009 Finite element exterior calculus for parabolic problems. Zbl 1362.65100 Arnold, Douglas N.; Chen, Hongtao 4 2017 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 Nefarious numbers. Zbl 1223.01042 Arnold, Douglas N.; Fowler, Kristine K. 2 2011 On the consistency of the combinatorial codifferential. Zbl 1298.58003 Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 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 6 2022 Complexes from complexes. Zbl 1520.58011 Arnold, Douglas N.; Hu, Kaibo 27 2021 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175 Arnold, Douglas; Guzmán, Johnny 6 2021 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182 Arnold, Douglas N.; Walker, Shawn W. 11 2020 Localization of eigenfunctions via an effective potential. Zbl 1432.35061 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 38 2019 Computing spectra without solving eigenvalue problems. Zbl 1420.81009 Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 29 2019 Finite element exterior calculus. Zbl 1506.65001 Arnold, Douglas N. 104 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 36 2015 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096 Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 21 2015 Finite element differential forms on cubical meshes. Zbl 1297.65142 Arnold, Douglas N.; Awanou, Gerard 35 2014 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033 Arnold, Douglas N.; Lee, Jeonghun J. 25 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 25 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. 19 2013 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100 Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 20 2012 The serendipity family of finite elements. Zbl 1218.65125 Arnold, Douglas N.; Awanou, Gerard 70 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 288 2010 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 55 2009 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132 Arnold, Douglas N.; Rognes, Marie E. 5 2009 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013 Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 121 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 173 2007 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396 Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 30 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 462 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 42 2006 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 40 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 21 2006 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 120 2005 Rectangular mixed finite elements for elasticity. Zbl 1077.74044 Arnold, Douglas N.; Awanou, Gerard 58 2005 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068 Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 45 2005 Nonconforming mixed elements for elasticity. Zbl 1057.74036 Arnold, Douglas N.; Winther, Ragnar 63 2003 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388 Arnold, Douglas N.; Winther, Ragnar 9 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 1,517 2002 Mixed finite elements for elasticity. Zbl 1090.74051 Arnold, Douglas N.; Winther, Ragnar 230 2002 Approximation by quadrilateral finite elements. Zbl 0993.65125 Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 117 2002 Differential complexes and numerical stability. Zbl 1023.65113 Arnold, Douglas N. 35 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 134 2000 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127 Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 86 2000 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116 Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 54 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. 15 1999 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078 Arnold, D. N.; Falk, R. S.; Winther, R. 12 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. 103 1997 Locking-free finite element methods for shells. Zbl 0854.65095 Arnold, Douglas N.; Brezzi, Franco 27 1997 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060 Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 22 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 5 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 31 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. 11 1991 Mixed finite element methods for elliptic problems. Zbl 0729.73198 Arnold, Douglas N. 63 1990 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042 Arnold, Douglas N.; Falk, Richard S. 47 1990 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040 Arnold, Douglas N.; Falk, Richard S. 144 1989 Coercivity of the single layer heat potential. Zbl 0672.65092 Arnold, Douglas N.; Noon, Patrick J. 24 1989 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208 Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 55 1988 A new mixed formulation for elasticity. Zbl 0621.73102 Arnold, Douglas N.; Falk, Richard S. 45 1988 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067 Cheng, R. S.-C.; Arnold, D. N. 7 1988 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012 Arnold, Douglas N.; Falk, Richard S. 25 1987 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078 Arnold, D. N.; Brezzi, F. 404 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. 505 1984 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074 Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 204 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. 146 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. 73 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. 782 1982 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028 Arnold, Douglas N.; Winther, Ragnar 16 1982 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092 Arnold, D. N.; Wendland, W. L. 8 1982 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066 Arnold, Douglas N. 83 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 52 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. 8 1979 all cited Publications top 5 cited Publications all top 5 Cited by 4,911 Authors 57 Cockburn, Bernardo 54 Gatica, Gabriel N. 50 Zhang, Shangyou 46 Ye, Xiu 45 Antonietti, Paola Francesca 37 Brezzi, Franco 34 Di Pietro, Daniele Antonio 33 Hu, Jun 32 Beirão da Veiga, Lourenço 32 Huang, Xuehai 32 Schöberl, Joachim 31 Carstensen, Carsten 31 Hughes, Thomas J. R. 31 Ruiz-Baier, Ricardo 31 Zhang, Zhimin 30 Hiptmair, Ralf 29 Arnold, Douglas Norman 29 Bassi, Francesco 29 Sayas, Francisco-Javier 28 Chen, Long 28 Marini, Luisa Donatella 28 Xu, Jinchao 27 He, Yinnian 27 Meddahi, Salim 26 Chen, Zhangxin 26 Guzmán, Johnny 26 Lovadina, Carlo 26 Rivière, Beatrice M. 25 Brenner, Susanne Cecelia 25 Stenberg, Rolf 25 Wheeler, Mary Fanett 24 Schötzau, Dominik 24 Xie, Xiaoping 23 Mu, Lin 23 Park, Eun-Jae 23 Wang, Junping 23 Winther, Ragnar 23 Yotov, Ivan 23 Zikatanov, Ludmil T. 22 Franca, Leopoldo Luis Cabo Penna 22 Houston, Paul 22 Wang, Fei 21 Hu, Kaibo 21 Huang, Yunqing 20 Giani, Stefano 20 Rapetti, Francesca 20 Scovazzi, Guglielmo 20 Vohralík, Martin 19 Ern, Alexandre 19 Gerritsma, Marc I. 19 Gopalakrishnan, Jay 19 Hu, Xiaozhe 19 Lee, Jeonghun J. 19 Loula, Abimael Fernando Dourado 19 Pani, Amiya Kumar 18 Ainsworth, Mark 18 Chen, Shaochun 18 Christiansen, Snorre Harald 18 Crivellini, Andrea 18 Devloo, Philippe Remy Bernard 18 Evans, John A. 18 Han, Weimin 18 Kanschat, Guido 18 Marquez-Duran, Antonio M. 18 Neilan, Michael 18 Nordström, Jan 18 Perugia, Ilaria 18 Qiu, Weifeng 18 Shang, Yueqiang 18 Vassilevski, Panayot Spirov 18 Wohlmuth, Barbara I. 17 Gudi, Thirupathi 17 Kwak, Do Young 17 Larson, Mats G. 17 Nordbotten, Jan Martin 17 Peraire, Jaime 17 Reddy, B. Dayanand 16 Badia, Santiago 16 Boffi, Daniele 16 Calo, Victor Manuel 16 Gomes, Sônia Maria 16 Kraus, Johannes K. 16 Russo, Alessandro 16 Schwab, Christoph 15 Botti, Lorenzo 15 Buffa, Annalisa 15 Colombo, Alessandro G. 15 Demkowicz, Leszek 15 Dolejší, Vít 15 Duan, Huoyuan 15 Falk, Richard S. 15 Ghidoni, Antonio 15 Kirby, Robert C. 15 Lederer, Philip Lukas 15 Nguyen, Ngoc Cuong 15 Oyarzúa, Ricardo 15 Shi, Zhongci 15 Sonnendrücker, Eric 15 Sung, Li-Yeng 15 Wang, Yanqiu ...and 4,811 more Authors all top 5 Cited in 299 Serials 563 Computer Methods in Applied Mechanics and Engineering 379 Journal of Computational Physics 297 Journal of Scientific Computing 232 Computers & Mathematics with Applications 214 Journal of Computational and Applied Mathematics 202 Numerische Mathematik 198 Mathematics of Computation 154 International Journal for Numerical Methods in Engineering 134 Applied Numerical Mathematics 130 SIAM Journal on Scientific Computing 125 Numerical Methods for Partial Differential Equations 113 SIAM Journal on Numerical Analysis 86 Computers and Fluids 77 Applied Mathematics and Computation 74 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 62 Computational Mechanics 62 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 62 Advances in Computational Mathematics 45 Calcolo 40 Computational Methods in Applied Mathematics 39 International Journal for Numerical Methods in Fluids 36 Computational Geosciences 32 Advances in Applied Mathematics and Mechanics 31 Mathematics and Computers in Simulation 31 Numerical Linear Algebra with Applications 31 International Journal of Numerical Analysis and Modeling 28 Numerical Algorithms 26 RAIRO. Modélisation Mathématique et Analyse Numérique 26 Science China. Mathematics 25 Foundations of Computational Mathematics 24 Mathematical Methods in the Applied Sciences 23 BIT 23 Journal of Numerical Mathematics 22 Journal of Mathematical Analysis and Applications 22 Applied Mathematics Letters 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 21 Communications in Computational Physics 21 Communications on Applied Mathematics and Computation 20 Applied Mathematical Modelling 20 Computational and Applied Mathematics 19 Computer Physics Communications 19 Engineering Analysis with Boundary Elements 18 Communications in Numerical Methods in Engineering 17 Applicable Analysis 17 Journal of Integral Equations and Applications 17 Japan Journal of Industrial and Applied Mathematics 16 International Journal of Computer Mathematics 15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 15 International Journal of Computational Methods 15 SMAI Journal of Computational Mathematics 14 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 13 Numerical Functional Analysis and Optimization 13 Results in Applied Mathematics 12 Applications of Mathematics 12 International Journal of Computational Fluid Dynamics 10 Acta Mechanica 10 Computing 10 Archives of Computational Methods in Engineering 10 Journal of Applied Mathematics and Computing 9 Mathematical Problems in Engineering 9 European Journal of Mechanics. A. Solids 9 Communications in Nonlinear Science and Numerical Simulation 9 Acta Numerica 8 Integral Equations and Operator Theory 8 Journal of Computational Mathematics 8 ETNA. Electronic Transactions on Numerical Analysis 8 Computing and Visualization in Science 8 Oberwolfach Reports 7 SIAM Review 7 Abstract and Applied Analysis 7 Discrete and Continuous Dynamical Systems. Series B 6 ACM Transactions on Mathematical Software 6 Journal of Elasticity 6 Multiscale Modeling & Simulation 6 East Asian Journal on Applied Mathematics 6 Electronic Research Archive 5 Journal of Mathematical Physics 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Communications in Partial Differential Equations 5 Journal of Nonlinear Science 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 Discrete and Continuous Dynamical Systems. Series S 5 GEM - International Journal on Geomathematics 5 Journal of the Korean Society for Industrial and Applied Mathematics 5 S\(\vec{\text{e}}\)MA Journal 5 Journal of Applied Analysis and Computation 5 Mathematics in Engineering 4 Archive for Rational Mechanics and Analysis 4 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 4 Meccanica 4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Applied Mathematics and Mechanics. (English Edition) 4 Computer Aided Geometric Design 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Vietnam Journal of Mathematics 4 Journal of Inequalities and Applications 4 Engineering Computations ...and 199 more Serials all top 5 Cited in 56 Fields 3,790 Numerical analysis (65-XX) 1,781 Partial differential equations (35-XX) 1,498 Fluid mechanics (76-XX) 1,126 Mechanics of deformable solids (74-XX) 230 Optics, electromagnetic theory (78-XX) 129 Global analysis, analysis on manifolds (58-XX) 124 Calculus of variations and optimal control; optimization (49-XX) 81 Geophysics (86-XX) 80 Statistical mechanics, structure of matter (82-XX) 79 Integral equations (45-XX) 64 Classical thermodynamics, heat transfer (80-XX) 60 Biology and other natural sciences (92-XX) 51 Operator theory (47-XX) 48 Approximations and expansions (41-XX) 44 Computer science (68-XX) 35 Potential theory (31-XX) 34 Differential geometry (53-XX) 28 Quantum theory (81-XX) 27 Ordinary differential equations (34-XX) 27 Functional analysis (46-XX) 23 Dynamical systems and ergodic theory (37-XX) 22 Probability theory and stochastic processes (60-XX) 18 Systems theory; control (93-XX) 17 Operations research, mathematical programming (90-XX) 16 Linear and multilinear algebra; matrix theory (15-XX) 14 Real functions (26-XX) 14 Relativity and gravitational theory (83-XX) 12 General and overarching topics; collections (00-XX) 12 Harmonic analysis on Euclidean spaces (42-XX) 12 Mechanics of particles and systems (70-XX) 10 Convex and discrete geometry (52-XX) 10 Algebraic topology (55-XX) 10 Statistics (62-XX) 9 Combinatorics (05-XX) 9 Algebraic geometry (14-XX) 8 Information and communication theory, circuits (94-XX) 7 Functions of a complex variable (30-XX) 7 Difference and functional equations (39-XX) 6 Manifolds and cell complexes (57-XX) 5 History and biography (01-XX) 5 Measure and integration (28-XX) 5 Special functions (33-XX) 4 Geometry (51-XX) 4 Astronomy and astrophysics (85-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Group theory and generalizations (20-XX) 3 Mathematics education (97-XX) 2 Category theory; homological algebra (18-XX) 2 Several complex variables and analytic spaces (32-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 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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