Edit Profile Arnold, Douglas Norman Compute Distance To: Compute Author ID: arnold.douglas-n Published as: Arnold, D. N.; Arnold, Douglas; Arnold, Douglas N. Homepage: http://www-users.math.umn.edu/~arnold/ External Links: MGP · Wikidata · ORCID · dblp · GND Documents Indexed: 88 Publications since 1979, including 2 Books 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 Fowler, Kristine K. 3 Mukherjee, Arup 3 Wendland, Wolfgang L. 2 Babuška, Ivo 2 Cockburn, Bernardo 2 David, Guy 2 Filoche, Marcel 2 Jerison, David S. 2 Liu, Xiaobo 2 Mayboroda, Svitlana 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 Guzmán, Johnny 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 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 1 Archive for Rational Mechanics and Analysis 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 Foundations of Computational Mathematics 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 CBMS-NSF Regional Conference Series in Applied Mathematics 1 The IMA Volumes in Mathematics and its Applications all top 5 Fields 59 Numerical analysis (65-XX) 41 Partial differential equations (35-XX) 38 Mechanics of deformable solids (74-XX) 9 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 79 Publications have been cited 5,023 times in 3,264 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 1,054 2002 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060Arnold, Douglas N. 545 1982 A stable finite element for the Stokes equations. Zbl 0593.76039Arnold, D. N.; Brezzi, F.; Fortin, M. 360 1984 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078Arnold, D. N.; Brezzi, F. 283 1985 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 269 2006 Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 166 2010 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 164 1984 Mixed finite elements for elasticity. Zbl 1090.74051Arnold, Douglas N.; Winther, Ragnar 152 2002 A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040Arnold, Douglas N.; Falk, Richard S. 129 1989 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 121 1984 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 108 2007 Approximation by quadrilateral finite elements. Zbl 0993.65125Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 90 2002 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 75 2005 Multigrid in H(div) and H(curl). Zbl 0974.65113Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 75 2000 Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066Arnold, Douglas N. 73 1981 On the asymptotic convergence of collocation methods. Zbl 0541.65075Arnold, Douglas N.; Wendland, Wolfgang L. 70 1983 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 69 2008 Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112Arnold, Douglas N.; Falk, Richard S.; Winther, R. 66 1997 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 65 2000 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077Arnold, Douglas N.; Wendland, Wolfgang L. 64 1985 Mixed finite element methods for elliptic problems. Zbl 0729.73198Arnold, Douglas N. 51 1990 A new mixed formulation for elasticity. Zbl 0621.73102Arnold, Douglas N.; Falk, Richard S. 48 1988 Rectangular mixed finite elements for elasticity. Zbl 1077.74044Arnold, Douglas N.; Awanou, Gerard 46 2005 Nonconforming mixed elements for elasticity. Zbl 1057.74036Arnold, Douglas N.; Winther, Ragnar 45 2003 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 44 2000 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 44 1988 The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042Arnold, Douglas N.; Falk, Richard S. 43 1990 The serendipity family of finite elements. Zbl 1218.65125Arnold, Douglas N.; Awanou, Gerard 40 2011 Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027Arnold, Douglas N.; Falk, Richard S. 37 1996 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 33 2005 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 31 2009 A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087Arnold, Douglas N. 28 1983 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 26 1981 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 25 2007 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 25 2006 Locking-free finite element methods for shells. Zbl 0854.65095Arnold, Douglas N.; Brezzi, Franco 25 1997 Finite element differential forms on cubical meshes. Zbl 1297.65142Arnold, Douglas N.; Awanou, Gerard 23 2014 Differential complexes and numerical stability. Zbl 1023.65113Arnold, Douglas N. 22 2002 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058Arnold, Douglas N.; Brezzi, Franco 22 1993 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 21 2002 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117Arnold, Douglas N.; Liu, Xiaobo 21 1995 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069Arnold, Douglas N.; Saranen, Jukka 21 1984 Coercivity of the single layer heat potential. Zbl 0672.65092Arnold, Douglas N.; Noon, Patrick J. 20 1989 Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012Arnold, Douglas N.; Falk, Richard S. 20 1987 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 19 1997 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 18 2015 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 17 2006 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068Arnold, Douglas N.; Falk, Richard S. 15 1997 Spaces of finite element differential forms. Zbl 1290.58003Arnold, Douglas N. 13 2013 Finite element approximation on quadrilateral meshes. Zbl 0999.76073Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia 13 2001 Derivation and justification of plate models by variational methods. Zbl 0958.74033Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L. 13 1999 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033Arnold, Douglas N.; Lee, Jeonghun J. 11 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 11 2014 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 1097.65003Arnold, Douglas N. (ed.); Bochev, Pavel B. (ed.); Lehoucq, Richard B. (ed.); Nicolaides, Roy A. (ed.); Shashkov, Mikhail (ed.) 11 2006 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 10 2015 Innovative finite element methods for plates. Zbl 0757.73048Arnold, Douglas N. 10 1991 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028Arnold, Douglas N.; Winther, Ragnar 10 1982 Finite element methods: Principles for their selection. Zbl 0513.73081Arnold, D. N.; Babuška, Ivo; Osborn, J. 9 1984 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 8 2012 Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388Arnold, Douglas N.; Winther, Ragnar 8 2003 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078Arnold, D. N.; Falk, R. S.; Winther, R. 6 1998 Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585Arnold, Douglas N.; Liu, Xiaobo 6 1997 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128Arnold, Douglas N. 6 1994 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 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094Arnold, D. N.; Douglas, Jim jun. 6 1979 Finite element exterior calculus. Zbl 07045589Arnold, Douglas N. 5 2018 Asymptotic estimates of hierarchical modeling. Zbl 1046.35024Arnold, Douglas N.; Madureira, Alexandre L. 5 2003 Localization of eigenfunctions via an effective potential. Zbl 1432.35061Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 4 2019 Computing spectra without solving eigenvalue problems. Zbl 1420.81009Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 4 2019 Finite element exterior calculus for parabolic problems. Zbl 1362.65100Arnold, Douglas N.; Chen, Hongtao 2 2017 On the consistency of the combinatorial codifferential. Zbl 1298.58003Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur 2 2014 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132Arnold, Douglas N.; Rognes, Marie E. 2 2009 Möbius transformations revealed. Zbl 1200.30036Arnold, Douglas N.; Rogness, Jonathan 2 2008 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134Arnold, Douglas N.; Tarfulea, Nicolae 2 2007 Finite element exterior calculus with lower-order terms. Zbl 1364.65236Arnold, Douglas N.; Li, Lizao 1 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 Localization of eigenfunctions via an effective potential. Zbl 1432.35061Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 4 2019 Computing spectra without solving eigenvalue problems. Zbl 1420.81009Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana 4 2019 Finite element exterior calculus. Zbl 07045589Arnold, Douglas N. 5 2018 Finite element exterior calculus for parabolic problems. Zbl 1362.65100Arnold, Douglas N.; Chen, Hongtao 2 2017 Finite element exterior calculus with lower-order terms. Zbl 1364.65236Arnold, Douglas N.; Li, Lizao 1 2017 Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca 18 2015 Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng 10 2015 Finite element differential forms on cubical meshes. Zbl 1297.65142Arnold, Douglas N.; Awanou, Gerard 23 2014 Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033Arnold, Douglas N.; Lee, Jeonghun J. 11 2014 Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 11 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. 13 2013 Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay 8 2012 The serendipity family of finite elements. Zbl 1218.65125Arnold, Douglas N.; Awanou, Gerard 40 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 166 2010 Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 31 2009 Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132Arnold, Douglas N.; Rognes, Marie E. 2 2009 Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar 69 2008 Möbius transformations revealed. Zbl 1200.30036Arnold, Douglas N.; Rogness, Jonathan 2 2008 Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 108 2007 Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella 25 2007 Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134Arnold, Douglas N.; Tarfulea, Nicolae 2 2007 Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 269 2006 Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 25 2006 Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 17 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 1097.65003Arnold, Douglas N. (ed.); Bochev, Pavel B. (ed.); Lehoucq, Richard B. (ed.); Nicolaides, Roy A. (ed.); Shashkov, Mikhail (ed.) 11 2006 Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 75 2005 Rectangular mixed finite elements for elasticity. Zbl 1077.74044Arnold, Douglas N.; Awanou, Gerard 46 2005 A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella 33 2005 Nonconforming mixed elements for elasticity. Zbl 1057.74036Arnold, Douglas N.; Winther, Ragnar 45 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 1,054 2002 Mixed finite elements for elasticity. Zbl 1090.74051Arnold, Douglas N.; Winther, Ragnar 152 2002 Approximation by quadrilateral finite elements. Zbl 0993.65125Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S. 90 2002 Differential complexes and numerical stability. Zbl 1023.65113Arnold, Douglas N. 22 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 21 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 75 2000 Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella 65 2000 Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc 44 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. 13 1999 Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078Arnold, D. N.; Falk, R. S.; Winther, R. 6 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. 66 1997 Locking-free finite element methods for shells. Zbl 0854.65095Arnold, Douglas N.; Brezzi, Franco 25 1997 Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar 19 1997 Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068Arnold, Douglas N.; Falk, Richard S. 15 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. 37 1996 Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117Arnold, Douglas N.; Liu, Xiaobo 21 1995 On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128Arnold, Douglas N. 6 1994 Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058Arnold, Douglas N.; Brezzi, Franco 22 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. 51 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. 129 1989 Coercivity of the single layer heat potential. Zbl 0672.65092Arnold, Douglas N.; Noon, Patrick J. 20 1989 A new mixed formulation for elasticity. Zbl 0621.73102Arnold, Douglas N.; Falk, Richard S. 48 1988 Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael 44 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. 20 1987 Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078Arnold, D. N.; Brezzi, F. 283 1985 The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077Arnold, Douglas N.; Wendland, Wolfgang L. 64 1985 A stable finite element for the Stokes equations. Zbl 0593.76039Arnold, D. N.; Brezzi, F.; Fortin, M. 360 1984 PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun. 164 1984 A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P. 121 1984 On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069Arnold, Douglas N.; Saranen, Jukka 21 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. 28 1983 An interior penalty finite element method with discontinuous elements. Zbl 0482.65060Arnold, Douglas N. 545 1982 A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028Arnold, Douglas N.; Winther, Ragnar 10 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. 73 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 26 1981 Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094Arnold, D. N.; Douglas, Jim jun. 6 1979 all cited Publications top 5 cited Publications all top 5 Cited by 3,677 Authors 52 Cockburn, Bernardo 45 Gatica, Gabriel N. 33 Ye, Xiu 31 Beirão da Veiga, Lourenço 31 Brezzi, Franco 30 Hughes, Thomas J. R. 29 Sayas, Francisco-Javier 28 Carstensen, Carsten 27 Antonietti, Paola Francesca 27 Schötzau, Dominik 26 Zhang, Shangyou 25 Arnold, Douglas Norman 25 Bassi, Francesco 25 Hiptmair, Ralf 24 Houston, Paul 24 Wheeler, Mary Fanett 24 Xu, Jinchao 23 Chen, Zhangxin 23 Marini, Luisa Donatella 23 Stenberg, Rolf 23 Winther, Ragnar 22 Brenner, Susanne Cecelia 22 Franca, Leopoldo Luis Cabo Penna 21 Lovadina, Carlo 21 Rivière, Beatrice M. 20 Di Pietro, Daniele Antonio 20 Guzmán, Johnny 20 Meddahi, Salim 20 Zhang, Zhimin 19 Hu, Jun 18 Mu, Lin 18 Schöberl, Joachim 18 Xie, Xiaoping 17 Bazilevs, Yuri 17 Giani, Stefano 17 Loula, Abimael Fernando Dourado 17 Pani, Amiya Kumar 17 Park, Eun-Jae 17 Perugia, Ilaria 17 Ruiz-Baier, Ricardo 17 Wang, Junping 16 Chen, Long 16 Chen, Shaochun 16 Christiansen, Snorre Harald 16 Evans, John A. 16 Huang, Xuehai 16 Larson, Mats G. 16 Marquez-Duran, Antonio M. 16 Schwab, Christoph 16 Vohralík, Martin 16 Yotov, Ivan 16 Zikatanov, Ludmil T. 15 Buffa, Annalisa 15 Crivellini, Andrea 15 Gudi, Thirupathi 15 He, Yinnian 15 Huang, Yunqing 15 Neilan, Michael 15 Scovazzi, Guglielmo 15 Shi, Zhongci 15 Wohlmuth, Barbara I. 14 Kanschat, Guido 14 Qiu, Weifeng 14 Russo, Alessandro 14 Vassilevski, Panayot Spirov 14 Wendland, Wolfgang L. 14 Wihler, Thomas Pascal 13 Ainsworth, Mark 13 Boffi, Daniele 13 Dolejší, Vít 13 Falk, Richard S. 13 Karasözen, Bülent 13 Lamichhane, Bishnu Prasad 13 Li, Jian 13 Oyarzúa, Ricardo 13 Reddy, B. Dayanand 13 Sacco, Riccardo 13 Shu, Chi-Wang 13 Wang, Fei 12 Auricchio, Ferdinando 12 Chen, Jinru 12 Demkowicz, Leszek F. 12 Duan, Huoyuan 12 Ern, Alexandre 12 Liu, Gui-Rong 12 Nguyen, Ngoc Cuong 12 Uzunca, Murat 12 van der Vegt, Jaap J. W. 12 Wu, Haijun 11 Babuška, Ivo 11 Bochev, Pavel B. 11 Calo, Victor Manuel 11 Castillo, Paul E. 11 Codina, Ramon 11 Durán, Ricardo G. 11 Gillette, Andrew 11 Han, Weimin 11 Kraus, Johannes K. 11 Kwak, Do Young 11 Lee, Jeonghun J. ...and 3,577 more Authors all top 5 Cited in 221 Serials 460 Computer Methods in Applied Mechanics and Engineering 266 Journal of Computational Physics 220 Journal of Scientific Computing 184 Numerische Mathematik 173 Journal of Computational and Applied Mathematics 171 Mathematics of Computation 140 Computers & Mathematics with Applications 111 Applied Numerical Mathematics 84 International Journal for Numerical Methods in Engineering 79 Numerical Methods for Partial Differential Equations 75 SIAM Journal on Scientific Computing 71 SIAM Journal on Numerical Analysis 69 Applied Mathematics and Computation 68 Computers and Fluids 67 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 47 Computational Mechanics 41 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 34 Calcolo 29 Advances in Computational Mathematics 27 Computational Geosciences 26 International Journal for Numerical Methods in Fluids 26 RAIRO. Modélisation Mathématique et Analyse Numérique 23 Computational Methods in Applied Mathematics 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 20 Science China. Mathematics 19 Numerical Linear Algebra with Applications 18 Journal of Mathematical Analysis and Applications 18 Communications in Numerical Methods in Engineering 17 Applied Mathematics Letters 16 Journal of Integral Equations and Applications 16 Journal of Numerical Mathematics 15 BIT 15 Mathematics and Computers in Simulation 15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 14 Japan Journal of Industrial and Applied Mathematics 13 Applicable Analysis 13 Engineering Analysis with Boundary Elements 12 Mathematical Methods in the Applied Sciences 12 Numerical Functional Analysis and Optimization 12 Foundations of Computational Mathematics 11 Applied Mathematical Modelling 11 International Journal of Computational Methods 10 Computing 10 Applications of Mathematics 10 Numerical Algorithms 10 Archives of Computational Methods in Engineering 8 ETNA. Electronic Transactions on Numerical Analysis 8 SMAI Journal of Computational Mathematics 7 Acta Mechanica 7 Integral Equations and Operator Theory 7 Mathematical Problems in Engineering 7 Abstract and Applied Analysis 6 International Journal of Computer Mathematics 6 International Journal of Computational Fluid Dynamics 6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 6 European Journal of Mechanics. A. Solids 6 Journal of Applied Mathematics and Computing 5 SIAM Review 5 Journal of Mathematical Sciences (New York) 5 Computational and Applied Mathematics 5 Computing and Visualization in Science 5 Journal of Applied Mathematics 5 Multiscale Modeling & Simulation 5 Acta Numerica 5 Results in Applied Mathematics 4 Archive for Rational Mechanics and Analysis 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 Elasticity 4 International Journal of Numerical Methods for Heat & Fluid Flow 4 Engineering Computations 4 International Journal of Numerical Analysis and Modeling 4 Boundary Value Problems 4 Discrete and Continuous Dynamical Systems. Series S 4 Advances in Mathematical Physics 4 GEM - International Journal on Geomathematics 4 East Asian Journal on Applied Mathematics 3 Inverse Problems 3 Journal of Mathematical Physics 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 ACM Transactions on Graphics 3 Communications in Partial Differential Equations 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Nonlinear Science 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Journal of Inequalities and Applications 3 Communications in Nonlinear Science and Numerical Simulation 3 Discrete and Continuous Dynamical Systems. Series B 3 Advances in Difference Equations 3 Oberwolfach Reports 3 Acta Mechanica Sinica 3 Frontiers of Mathematics in China 3 Advances in Numerical Analysis 3 International Journal for Numerical Methods in Biomedical Engineering 3 S\(\vec{\text{e}}\)MA Journal 3 Journal of Theoretical Biology ...and 121 more Serials all top 5 Cited in 50 Fields 2,531 Numerical analysis (65-XX) 1,191 Partial differential equations (35-XX) 982 Fluid mechanics (76-XX) 840 Mechanics of deformable solids (74-XX) 154 Optics, electromagnetic theory (78-XX) 72 Calculus of variations and optimal control; optimization (49-XX) 67 Integral equations (45-XX) 63 Global analysis, analysis on manifolds (58-XX) 52 Geophysics (86-XX) 47 Statistical mechanics, structure of matter (82-XX) 46 Classical thermodynamics, heat transfer (80-XX) 42 Biology and other natural sciences (92-XX) 30 Operator theory (47-XX) 25 Ordinary differential equations (34-XX) 25 Approximations and expansions (41-XX) 23 Computer science (68-XX) 21 Potential theory (31-XX) 18 Functional analysis (46-XX) 15 Dynamical systems and ergodic theory (37-XX) 14 Differential geometry (53-XX) 12 Quantum theory (81-XX) 10 Probability theory and stochastic processes (60-XX) 10 Systems theory; control (93-XX) 8 Real functions (26-XX) 7 Linear and multilinear algebra; matrix theory (15-XX) 7 Functions of a complex variable (30-XX) 7 Relativity and gravitational theory (83-XX) 7 Information and communication theory, circuits (94-XX) 6 General and overarching topics; collections (00-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistics (62-XX) 5 History and biography (01-XX) 5 Difference and functional equations (39-XX) 5 Convex and discrete geometry (52-XX) 5 Algebraic topology (55-XX) 5 Mechanics of particles and systems (70-XX) 5 Operations research, mathematical programming (90-XX) 4 Algebraic geometry (14-XX) 3 Combinatorics (05-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 Special functions (33-XX) 2 Geometry (51-XX) 1 Commutative algebra (13-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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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