Edit Profile (opens in new tab) Arnold, Douglas Norman Compute Distance To: Compute 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: 90 Publications since 1979, including 1 Book 1 Contribution as Editor Co-Authors: 51 Co-Authors with 78 Joint Publications 1,499 Co-Co-Authors all top 5 Co-Authors 13 single-authored 24 Falk, Richard S. 16 Winther, Ragnar 9 Brezzi, Franco 6 Awanou, Gerard Michel 4 Boffi, Daniele 4 Douglas, Jim jun. 4 Madureira, Alexandre L. 4 Marini, Luisa Donatella 3 Filoche, Marcel 3 Fowler, Kristine K. 3 Mayboroda, Svitlana 3 Mukherjee, Arup 3 Wendland, Wolfgang L. 2 Babuška, Ivo 2 Cockburn, Bernardo 2 David, Guy 2 Guzmán, Johnny 2 Jerison, David S. 2 Liu, Xiaobo 2 Osborn, John E. 2 Pouly, Luc 1 Alessandrini, Stephan M. 1 Alessandrini, Stephen M. 1 Bochev, Pavel B. 1 Bonizzoni, Francesca 1 Chen, Hongtao 1 Cheng, R. S.-C. 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 Qiu, Weifeng 1 Rognes, Marie E. 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 Wang, Wei 1 Zhang, Sheng 1 Zhang, Shiwen 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 CBMS-NSF Regional Conference Series in Applied Mathematics 1 The IMA Volumes in Mathematics and its Applications all top 5 Fields 61 Numerical analysis (65-XX) 43 Partial differential equations (35-XX) 38 Mechanics of deformable solids (74-XX) 10 Global analysis, analysis on manifolds (58-XX) 5 Integral equations (45-XX) 5 Fluid mechanics (76-XX) 4 History and biography (01-XX) 3 General and overarching topics; collections (00-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 Statistical mechanics, structure of matter (82-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 Operator theory (47-XX) 1 Manifolds and cell complexes (57-XX) 1 Quantum theory (81-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 82 Publications have been cited 5,923 times in 3,821 Documents Cited by ▼ Year ▼ Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella 1,234 2002 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060Arnold, Douglas N. 654 1982 A stable finite element for the Stokes equations. Zbl 0593.76039Arnold, D. N.; Brezzi, F.; Fortin, M. 405 1984 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 344 2006 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078Arnold, D. N.; Brezzi, F. 335 1985 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 217 2010 Mixed finite elements for elasticity. Zbl 1090.74051Arnold, Douglas N.; Winther, Ragnar 189 2002 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 185 1984 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040Arnold, Douglas N.; Falk, Richard S. 135 1989 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 132 2007 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 130 1984 Approximation by quadrilateral finite elements. Zbl 0993.65125Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 104 2002 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 96 2008 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 95 2005 Multigrid in H(div) and H(curl). Zbl 0974.65113Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 92 2000 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066Arnold, Douglas N. 77 1981 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112Arnold, Douglas N.; Falk, Richard S.; Winther, R. 75 1997 On the asymptotic convergence of collocation methods. Zbl 0541.65075Arnold, Douglas N.; Wendland, Wolfgang L. 70 1983 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 69 2000 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077Arnold, Douglas N.; Wendland, Wolfgang L. 67 1985 Mixed finite element methods for elliptic problems. Zbl 0729.73198Arnold, Douglas N. 56 1990 Rectangular mixed finite elements for elasticity. Zbl 1077.74044Arnold, Douglas N.; Awanou, Gerard 53 2005 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 52 2000 Nonconforming mixed elements for elasticity. Zbl 1057.74036Arnold, Douglas N.; Winther, Ragnar 51 2003 The serendipity family of finite elements. Zbl 1218.65125Arnold, Douglas N.; Awanou, Gerard 51 2011 A new mixed formulation for elasticity. Zbl 0621.73102Arnold, Douglas N.; Falk, Richard S. 49 1988 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 47 1988 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042Arnold, Douglas N.; Falk, Richard S. 43 1990 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027Arnold, Douglas N.; Falk, Richard S. 39 1996 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 37 2005 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 36 2009 Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Zbl 0466.65062Arnold, Douglas N.; Douglas, Jim jun.; Thomee, Vidar 36 1981 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 31 2006 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087Arnold, Douglas N. 29 1983 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 27 2007 Finite element exterior calculus. Zbl 07045589Arnold, Douglas N. 27 2018 Finite element differential forms on cubical meshes. Zbl 1297.65142Arnold, Douglas N.; Awanou, Gerard 27 2014 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117Arnold, Douglas N.; Liu, Xiaobo 27 1995 Locking-free finite element methods for shells. Zbl 0854.65095Arnold, Douglas N.; Brezzi, Franco 26 1997 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 23 2015 Differential complexes and numerical stability. Zbl 1023.65113Arnold, Douglas N. 23 2002 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058Arnold, Douglas N.; Brezzi, Franco 23 1993 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069Arnold, Douglas N.; Saranen, Jukka 22 1984 On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models. Zbl 1089.74595Arnold, Douglas N.; Madureira, Alexandre L.; Zhang, Sheng 22 2002 Coercivity of the single layer heat potential. Zbl 0672.65092Arnold, Douglas N.; Noon, Patrick J. 22 1989 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 21 2006 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012Arnold, Douglas N.; Falk, Richard S. 21 1987 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 20 1997 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033Arnold, Douglas N.; Lee, Jeonghun J. 19 2014 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068Arnold, Douglas N.; Falk, Richard S. 16 1997 Spaces of finite element differential forms. Zbl 1290.58003Arnold, Douglas N. 15 2013 Computing spectra without solving eigenvalue problems. Zbl 1420.81009Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 15 2019 Localization of eigenfunctions via an effective potential. Zbl 1432.35061Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 15 2019 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 15 2014 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 15 2015 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028Arnold, Douglas N.; Winther, Ragnar 14 1982 Derivation and justification of plate models by variational methods. Zbl 0958.74033Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 14 1999 Finite element approximation on quadrilateral meshes. Zbl 0999.76073Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 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 10 2006 Innovative finite element methods for plates. Zbl 0757.73048Arnold, Douglas N. 10 1991 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 9 2012 Finite element methods: Principles for their selection. Zbl 0513.73081Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388Arnold, Douglas N.; Winther, Ragnar 8 2003 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128Arnold, Douglas N. 8 1994 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094Arnold, D. N.; Douglas, Jim jun. 7 1979 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078Arnold, D. N.; Falk, R. S.; Winther, R. 7 1998 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067Cheng, R. S.-C.; Arnold, D. N. 6 1988 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092Arnold, D. N.; Wendland, W. L. 6 1982 Möbius transformations revealed. Zbl 1200.30036Arnold, Douglas N.; Rogness, Jonathan 6 2008 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585Arnold, Douglas N.; Liu, Xiaobo 6 1997 Complexes from complexes. Zbl 07458824Arnold, Douglas N.; Hu, Kaibo 6 2021 Asymptotic estimates of hierarchical modeling. Zbl 1046.35024Arnold, Douglas N.; Madureira, Alexandre L. 5 2003 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182Arnold, Douglas N.; Walker, Shawn W. 5 2020 Finite element exterior calculus for parabolic problems. Zbl 1362.65100Arnold, Douglas N.; Chen, Hongtao 4 2017 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132Arnold, Douglas N.; Rognes, Marie E. 3 2009 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134Arnold, Douglas N.; Tarfulea, Nicolae 3 2007 On the consistency of the combinatorial codifferential. Zbl 1298.58003Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 Finite element exterior calculus with lower-order terms. Zbl 1364.65236Arnold, Douglas N.; Li, Lizao 2 2017 Nefarious numbers. Zbl 1223.01042Arnold, Douglas N.; Fowler, Kristine K. 1 2011 Numerical problems in general relativity. Zbl 0976.83002Arnold, Douglas N. 1 2000 Adaptive finite elements and colliding black holes. Zbl 0902.65080Arnold, D. N.; Mukherjee, A.; Pouly, L. 1 1998 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175Arnold, Douglas; Guzmán, Johnny 1 2021 Complexes from complexes. Zbl 07458824Arnold, Douglas N.; Hu, Kaibo 6 2021 Local \(L^2\)-bounded commuting projections in FEEC. Zbl 1483.65175Arnold, Douglas; Guzmán, Johnny 1 2021 The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182Arnold, Douglas N.; Walker, Shawn W. 5 2020 Computing spectra without solving eigenvalue problems. Zbl 1420.81009Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 15 2019 Localization of eigenfunctions via an effective potential. Zbl 1432.35061Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 15 2019 Finite element exterior calculus. Zbl 07045589Arnold, Douglas N. 27 2018 Finite element exterior calculus for parabolic problems. Zbl 1362.65100Arnold, Douglas N.; Chen, Hongtao 4 2017 Finite element exterior calculus with lower-order terms. Zbl 1364.65236Arnold, Douglas N.; Li, Lizao 2 2017 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 23 2015 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 15 2015 Finite element differential forms on cubical meshes. Zbl 1297.65142Arnold, Douglas N.; Awanou, Gerard 27 2014 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033Arnold, Douglas N.; Lee, Jeonghun J. 19 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 15 2014 On the consistency of the combinatorial codifferential. Zbl 1298.58003Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 Spaces of finite element differential forms. Zbl 1290.58003Arnold, Douglas N. 15 2013 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 9 2012 The serendipity family of finite elements. Zbl 1218.65125Arnold, Douglas N.; Awanou, Gerard 51 2011 Nefarious numbers. Zbl 1223.01042Arnold, Douglas N.; Fowler, Kristine K. 1 2011 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 217 2010 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 36 2009 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132Arnold, Douglas N.; Rognes, Marie E. 3 2009 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 96 2008 Möbius transformations revealed. Zbl 1200.30036Arnold, Douglas N.; Rogness, Jonathan 6 2008 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 132 2007 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 27 2007 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134Arnold, Douglas N.; Tarfulea, Nicolae 3 2007 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 344 2006 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 31 2006 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 21 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 10 2006 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 95 2005 Rectangular mixed finite elements for elasticity. Zbl 1077.74044Arnold, Douglas N.; Awanou, Gerard 53 2005 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 37 2005 Nonconforming mixed elements for elasticity. Zbl 1057.74036Arnold, Douglas N.; Winther, Ragnar 51 2003 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388Arnold, Douglas N.; Winther, Ragnar 8 2003 Asymptotic estimates of hierarchical modeling. Zbl 1046.35024Arnold, Douglas N.; Madureira, Alexandre L. 5 2003 Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella 1,234 2002 Mixed finite elements for elasticity. Zbl 1090.74051Arnold, Douglas N.; Winther, Ragnar 189 2002 Approximation by quadrilateral finite elements. Zbl 0993.65125Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 104 2002 Differential complexes and numerical stability. Zbl 1023.65113Arnold, Douglas N. 23 2002 On the range of applicability of the Reissner–Mindlin and Kirchhoff–Love plate bending models. Zbl 1089.74595Arnold, Douglas N.; Madureira, Alexandre L.; Zhang, Sheng 22 2002 Finite element approximation on quadrilateral meshes. Zbl 0999.76073Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 Multigrid in H(div) and H(curl). Zbl 0974.65113Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 92 2000 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 69 2000 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 52 2000 Numerical problems in general relativity. Zbl 0976.83002Arnold, Douglas N. 1 2000 Derivation and justification of plate models by variational methods. Zbl 0958.74033Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 14 1999 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078Arnold, D. N.; Falk, R. S.; Winther, R. 7 1998 Adaptive finite elements and colliding black holes. Zbl 0902.65080Arnold, D. N.; Mukherjee, A.; Pouly, L. 1 1998 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112Arnold, Douglas N.; Falk, Richard S.; Winther, R. 75 1997 Locking-free finite element methods for shells. Zbl 0854.65095Arnold, Douglas N.; Brezzi, Franco 26 1997 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 20 1997 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068Arnold, Douglas N.; Falk, Richard S. 16 1997 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585Arnold, Douglas N.; Liu, Xiaobo 6 1997 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027Arnold, Douglas N.; Falk, Richard S. 39 1996 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117Arnold, Douglas N.; Liu, Xiaobo 27 1995 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128Arnold, Douglas N. 8 1994 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058Arnold, Douglas N.; Brezzi, Franco 23 1993 Innovative finite element methods for plates. Zbl 0757.73048Arnold, Douglas N. 10 1991 Mixed finite element methods for elliptic problems. Zbl 0729.73198Arnold, Douglas N. 56 1990 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042Arnold, Douglas N.; Falk, Richard S. 43 1990 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040Arnold, Douglas N.; Falk, Richard S. 135 1989 Coercivity of the single layer heat potential. Zbl 0672.65092Arnold, Douglas N.; Noon, Patrick J. 22 1989 A new mixed formulation for elasticity. Zbl 0621.73102Arnold, Douglas N.; Falk, Richard S. 49 1988 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 47 1988 The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067Cheng, R. S.-C.; Arnold, D. N. 6 1988 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012Arnold, Douglas N.; Falk, Richard S. 21 1987 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078Arnold, D. N.; Brezzi, F. 335 1985 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077Arnold, Douglas N.; Wendland, Wolfgang L. 67 1985 A stable finite element for the Stokes equations. Zbl 0593.76039Arnold, D. N.; Brezzi, F.; Fortin, M. 405 1984 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 185 1984 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 130 1984 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069Arnold, Douglas N.; Saranen, Jukka 22 1984 Finite element methods: Principles for their selection. Zbl 0513.73081Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 On the asymptotic convergence of collocation methods. Zbl 0541.65075Arnold, Douglas N.; Wendland, Wolfgang L. 70 1983 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087Arnold, Douglas N. 29 1983 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060Arnold, Douglas N. 654 1982 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028Arnold, Douglas N.; Winther, Ragnar 14 1982 Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092Arnold, D. N.; Wendland, W. L. 6 1982 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066Arnold, Douglas N. 77 1981 Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Zbl 0466.65062Arnold, Douglas N.; Douglas, Jim jun.; Thomee, Vidar 36 1981 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094Arnold, D. N.; Douglas, Jim jun. 7 1979 all cited Publications top 5 cited Publications all top 5 Cited by 4,030 Authors 54 Cockburn, Bernardo 48 Gatica, Gabriel N. 40 Ye, Xiu 37 Zhang, Shangyou 35 Antonietti, Paola Francesca 32 Beirão da Veiga, Lourenço 32 Brezzi, Franco 32 Hughes, Thomas J. R. 31 Carstensen, Carsten 29 Sayas, Francisco-Javier 28 Arnold, Douglas Norman 28 Hiptmair, Ralf 28 Xu, Jinchao 27 Schötzau, Dominik 26 Bassi, Francesco 26 Di Pietro, Daniele Antonio 25 Houston, Paul 25 Lovadina, Carlo 25 Marini, Luisa Donatella 25 Stenberg, Rolf 25 Wheeler, Mary Fanett 24 Chen, Zhangxin 24 Guzmán, Johnny 23 Meddahi, Salim 23 Ruiz-Baier, Ricardo 23 Schöberl, Joachim 23 Winther, Ragnar 23 Zhang, Zhimin 22 Brenner, Susanne Cecelia 22 Franca, Leopoldo Luis Cabo Penna 22 Hu, Jun 22 Huang, Xuehai 22 Rivière, Beatrice M. 21 Chen, Long 21 Xie, Xiaoping 20 He, Yinnian 20 Mu, Lin 20 Park, Eun-Jae 20 Yotov, Ivan 19 Giani, Stefano 19 Pani, Amiya Kumar 19 Wang, Junping 19 Zikatanov, Ludmil T. 18 Crivellini, Andrea 18 Huang, Yunqing 18 Marquez-Duran, Antonio M. 18 Perugia, Ilaria 18 Vohralík, Martin 18 Wang, Fei 17 Bazilevs, Yuri 17 Ern, Alexandre 17 Kanschat, Guido 17 Loula, Abimael Fernando Dourado 16 Boffi, Daniele 16 Chen, Shaochun 16 Christiansen, Snorre Harald 16 Evans, John A. 16 Gudi, Thirupathi 16 Larson, Mats G. 16 Neilan, Michael 16 Qiu, Weifeng 16 Vassilevski, Panayot Spirov 16 Wohlmuth, Barbara I. 15 Ainsworth, Mark 15 Oyarzúa, Ricardo 15 Scovazzi, Guglielmo 15 Shang, Yueqiang 15 Shi, Zhongci 14 Botti, Lorenzo 14 Buffa, Annalisa 14 Dolejší, Vít 14 Gerritsma, Marc I. 14 Han, Weimin 14 Kraus, Johannes K. 14 Reddy, B. Dayanand 14 Russo, Alessandro 14 Schwab, Christoph 14 Wendland, Wolfgang L. 13 Colombo, Alessandro G. 13 Duan, Huoyuan 13 Falk, Richard S. 13 Hu, Kaibo 13 Hu, Xiaozhe 13 Karasözen, Bülent 13 Lamichhane, Bishnu Prasad 13 Lee, Jeonghun J. 13 Nguyen, Ngoc Cuong 13 Nordström, Jan 13 Sacco, Riccardo 13 Shu, Chi-Wang 13 Uzunca, Murat 13 van der Vegt, Jaap J. W. 13 Wihler, Thomas Pascal 13 Wu, Haijun 12 Arbogast, Todd 12 Auricchio, Ferdinando 12 Badia, Santiago 12 Barrios, Tomás P. 12 Bustinza, Rommel A. 12 Calo, Victor Manuel ...and 3,930 more Authors all top 5 Cited in 257 Serials 486 Computer Methods in Applied Mechanics and Engineering 309 Journal of Computational Physics 258 Journal of Scientific Computing 195 Numerische Mathematik 186 Journal of Computational and Applied Mathematics 184 Mathematics of Computation 176 Computers & Mathematics with Applications 116 Applied Numerical Mathematics 102 SIAM Journal on Scientific Computing 89 SIAM Journal on Numerical Analysis 84 International Journal for Numerical Methods in Engineering 79 Numerical Methods for Partial Differential Equations 73 Computers and Fluids 73 Applied Mathematics and Computation 73 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 56 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 55 Computational Mechanics 42 Advances in Computational Mathematics 38 Calcolo 33 Computational Geosciences 32 Computational Methods in Applied Mathematics 28 Advances in Applied Mathematics and Mechanics 26 International Journal for Numerical Methods in Fluids 26 RAIRO. Modélisation Mathématique et Analyse Numérique 23 Numerical Algorithms 23 Science China. Mathematics 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 21 International Journal of Numerical Analysis and Modeling 20 Journal of Mathematical Analysis and Applications 20 Applied Mathematics Letters 20 Journal of Numerical Mathematics 19 Mathematics and Computers in Simulation 19 Numerical Linear Algebra with Applications 18 BIT 18 Communications in Numerical Methods in Engineering 17 Journal of Integral Equations and Applications 17 Foundations of Computational Mathematics 16 Japan Journal of Industrial and Applied Mathematics 16 Applied Mathematical Modelling 16 Engineering Analysis with Boundary Elements 16 Communications in Computational Physics 15 Applicable Analysis 15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 14 Computational and Applied Mathematics 14 Communications on Applied Mathematics and Computation 13 Numerical Functional Analysis and Optimization 13 International Journal of Computer Mathematics 12 Mathematical Methods in the Applied Sciences 12 International Journal of Computational Methods 11 Applications of Mathematics 11 SMAI Journal of Computational Mathematics 10 Computing 10 International Journal of Computational Fluid Dynamics 10 Archives of Computational Methods in Engineering 8 Acta Mechanica 8 Integral Equations and Operator Theory 8 ETNA. Electronic Transactions on Numerical Analysis 8 Journal of Applied Mathematics and Computing 7 Mathematical Problems in Engineering 7 Abstract and Applied Analysis 7 European Journal of Mechanics. A. Solids 6 Journal of Elasticity 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 Discrete and Continuous Dynamical Systems. Series B 6 Electronic Research Archive 5 SIAM Review 5 Journal of Mathematical Sciences (New York) 5 Computing and Visualization in Science 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Journal of Applied Mathematics 5 Multiscale Modeling & Simulation 5 Acta Numerica 5 Advances in Difference Equations 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 Communications in Partial Differential Equations 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Vietnam Journal of Mathematics 4 Engineering Computations 4 Oberwolfach Reports 4 Boundary Value Problems 4 Discrete and Continuous Dynamical Systems. Series S 4 Advances in Mathematical Physics 4 GEM - International Journal on Geomathematics 4 S\(\vec{\text{e}}\)MA Journal 3 Inverse Problems 3 Journal of Engineering Mathematics 3 Journal of the Mechanics and Physics of Solids 3 Zhurnal Vychislitel’noĭ Matematiki i Matematicheskoĭ Fiziki 3 ACM Transactions on Mathematical Software 3 Annali di Matematica Pura ed Applicata. Serie Quarta 3 Transactions of the American Mathematical Society 3 Journal of Computational Mathematics 3 ACM Transactions on Graphics ...and 157 more Serials all top 5 Cited in 53 Fields 3,009 Numerical analysis (65-XX) 1,425 Partial differential equations (35-XX) 1,189 Fluid mechanics (76-XX) 951 Mechanics of deformable solids (74-XX) 180 Optics, electromagnetic theory (78-XX) 87 Calculus of variations and optimal control; optimization (49-XX) 83 Global analysis, analysis on manifolds (58-XX) 73 Integral equations (45-XX) 67 Geophysics (86-XX) 63 Statistical mechanics, structure of matter (82-XX) 49 Classical thermodynamics, heat transfer (80-XX) 45 Biology and other natural sciences (92-XX) 34 Operator theory (47-XX) 33 Computer science (68-XX) 32 Approximations and expansions (41-XX) 26 Potential theory (31-XX) 26 Ordinary differential equations (34-XX) 20 Differential geometry (53-XX) 19 Dynamical systems and ergodic theory (37-XX) 19 Quantum theory (81-XX) 18 Functional analysis (46-XX) 16 Probability theory and stochastic processes (60-XX) 14 Systems theory; control (93-XX) 12 Real functions (26-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Mechanics of particles and systems (70-XX) 10 Relativity and gravitational theory (83-XX) 10 Operations research, mathematical programming (90-XX) 9 Statistics (62-XX) 7 General and overarching topics; collections (00-XX) 7 Functions of a complex variable (30-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Information and communication theory, circuits (94-XX) 6 Convex and discrete geometry (52-XX) 6 Algebraic topology (55-XX) 5 History and biography (01-XX) 5 Combinatorics (05-XX) 5 Algebraic geometry (14-XX) 4 Difference and functional equations (39-XX) 3 Special functions (33-XX) 3 Manifolds and cell complexes (57-XX) 3 Astronomy and astrophysics (85-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Measure and integration (28-XX) 2 Geometry (51-XX) 1 Field theory and polynomials (12-XX) 1 Commutative algebra (13-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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