## Arnold, Douglas Norman

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 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: 89 Publications since 1979, including 1 Book 1 Contribution as Editor Co-Authors: 49 Co-Authors with 77 Joint Publications 1,462 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 Fowler, Kristine K. 3 Mukherjee, Arup 3 Wendland, Wolfgang L. 2 Babuška, Ivo 2 Cockburn, Bernardo 2 David, Guy 2 Filoche, Marcel 2 Guzmán, Johnny 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 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 Zhang, Sheng
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### 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 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

 60 Numerical analysis (65-XX) 42 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)

### Citations contained in zbMATH Open

81 Publications have been cited 5,712 times in 3,714 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
2002
An interior penalty finite element method with discontinuous elements. Zbl 0482.65060
Arnold, Douglas N.
1982
A stable finite element for the Stokes equations. Zbl 0593.76039
Arnold, D. N.; Brezzi, F.; Fortin, M.
1984
Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078
Arnold, D. N.; Brezzi, F.
1985
Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2006
Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2010
PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074
Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun.
1984
Mixed finite elements for elasticity. Zbl 1090.74051
Arnold, Douglas N.; Winther, Ragnar
2002
A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040
Arnold, Douglas N.; Falk, Richard S.
1989
A family of higher order mixed finite element methods for plane elasticity. Zbl 0558.73066
Arnold, Douglas N.; Douglas, Jim jun.; Gupta, Chaitan P.
1984
Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2007
Approximation by quadrilateral finite elements. Zbl 0993.65125
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
2002
Quadrilateral $$H$$(div) finite elements. Zbl 1086.65105
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
2005
Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
2008
Multigrid in H(div) and H(curl). Zbl 0974.65113
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2000
Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066
Arnold, Douglas N.
1981
Preconditioning in H $$(\operatorname{div})$$ and applications. Zbl 0870.65112
Arnold, Douglas N.; Falk, Richard S.; Winther, R.
1997
On the asymptotic convergence of collocation methods. Zbl 0541.65075
Arnold, Douglas N.; Wendland, Wolfgang L.
1983
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
2000
The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077
Arnold, Douglas N.; Wendland, Wolfgang L.
1985
Mixed finite element methods for elliptic problems. Zbl 0729.73198
Arnold, Douglas N.
1990
Rectangular mixed finite elements for elasticity. Zbl 1077.74044
Arnold, Douglas N.; Awanou, Gerard
2005
Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116
Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc
2000
Nonconforming mixed elements for elasticity. Zbl 1057.74036
Arnold, Douglas N.; Winther, Ragnar
2003
A new mixed formulation for elasticity. Zbl 0621.73102
Arnold, Douglas N.; Falk, Richard S.
1988
Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208
Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael
1988
The serendipity family of finite elements. Zbl 1218.65125
Arnold, Douglas N.; Awanou, Gerard
2011
The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042
Arnold, Douglas N.; Falk, Richard S.
1990
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027
Arnold, Douglas N.; Falk, Richard S.
1996
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
1981
Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2009
A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068
Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella
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
2006
A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087
Arnold, Douglas N.
1983
Finite element differential forms on cubical meshes. Zbl 1297.65142
Arnold, Douglas N.; Awanou, Gerard
2014
Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117
Arnold, Douglas N.; Liu, Xiaobo
1995
Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396
Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella
2007
Locking-free finite element methods for shells. Zbl 0854.65095
Arnold, Douglas N.; Brezzi, Franco
1997
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
2002
Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193
Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca
2015
Differential complexes and numerical stability. Zbl 1023.65113
Arnold, Douglas N.
2002
Finite element exterior calculus. Zbl 07045589
Arnold, Douglas N.
2018
Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058
Arnold, Douglas N.; Brezzi, Franco
1993
Coercivity of the single layer heat potential. Zbl 0672.65092
Arnold, Douglas N.; Noon, Patrick J.
1989
Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012
Arnold, Douglas N.; Falk, Richard S.
1987
On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069
Arnold, Douglas N.; Saranen, Jukka
1984
Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2006
Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
1997
Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033
Arnold, Douglas N.; Lee, Jeonghun J.
2014
Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068
Arnold, Douglas N.; Falk, Richard S.
1997
Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
2014
Spaces of finite element differential forms. Zbl 1290.58003
Arnold, Douglas N.
2013
Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096
Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng
2015
Derivation and justification of plate models by variational methods. Zbl 0958.74033
Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L.
1999
Computing spectra without solving eigenvalue problems. Zbl 1420.81009
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
2019
Finite element approximation on quadrilateral meshes. Zbl 0999.76073
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia
2001
Localization of eigenfunctions via an effective potential. Zbl 1432.35061
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
2019
A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028
Arnold, Douglas N.; Winther, Ragnar
1982
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
2006
Innovative finite element methods for plates. Zbl 0757.73048
Arnold, Douglas N.
1991
Finite element methods: Principles for their selection. Zbl 0513.73081
Arnold, D. N.; Babuška, Ivo; Osborn, J.
1984
On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128
Arnold, Douglas N.
1994
Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388
Arnold, Douglas N.; Winther, Ragnar
2003
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100
Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay
2012
Multigrid preconditioning in $$H(\text{div})$$ on non-convex polygons. Zbl 0922.65078
Arnold, D. N.; Falk, R. S.; Winther, R.
1998
Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094
Arnold, D. N.; Douglas, Jim jun.
1979
The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067
Cheng, R. S.-C.; Arnold, D. N.
1988
Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092
Arnold, D. N.; Wendland, W. L.
1982
Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585
Arnold, Douglas N.; Liu, Xiaobo
1997
Asymptotic estimates of hierarchical modeling. Zbl 1046.35024
Arnold, Douglas N.; Madureira, Alexandre L.
2003
Möbius transformations revealed. Zbl 1200.30036
Arnold, Douglas N.; Rogness, Jonathan
2008
The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182
Arnold, Douglas N.; Walker, Shawn W.
2020
Finite element exterior calculus for parabolic problems. Zbl 1362.65100
Arnold, Douglas N.; Chen, Hongtao
2017
Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134
Arnold, Douglas N.; Tarfulea, Nicolae
2007
Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132
Arnold, Douglas N.; Rognes, Marie E.
2009
On the consistency of the combinatorial codifferential. Zbl 1298.58003
Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur
2014
Finite element exterior calculus with lower-order terms. Zbl 1364.65236
Arnold, Douglas N.; Li, Lizao
2017
Complexes from complexes. Zbl 07458824
Arnold, Douglas N.; Hu, Kaibo
2021
Numerical problems in general relativity. Zbl 0976.83002
Arnold, Douglas N.
2000
Adaptive finite elements and colliding black holes. Zbl 0902.65080
Arnold, D. N.; Mukherjee, A.; Pouly, L.
1998
Nefarious numbers. Zbl 1223.01042
Arnold, Douglas N.; Fowler, Kristine K.
2011
Complexes from complexes. Zbl 07458824
Arnold, Douglas N.; Hu, Kaibo
2021
The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182
Arnold, Douglas N.; Walker, Shawn W.
2020
Computing spectra without solving eigenvalue problems. Zbl 1420.81009
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
2019
Localization of eigenfunctions via an effective potential. Zbl 1432.35061
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
2019
Finite element exterior calculus. Zbl 07045589
Arnold, Douglas N.
2018
Finite element exterior calculus for parabolic problems. Zbl 1362.65100
Arnold, Douglas N.; Chen, Hongtao
2017
Finite element exterior calculus with lower-order terms. Zbl 1364.65236
Arnold, Douglas N.; Li, Lizao
2017
Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193
Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca
2015
Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096
Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng
2015
Finite element differential forms on cubical meshes. Zbl 1297.65142
Arnold, Douglas N.; Awanou, Gerard
2014
Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033
Arnold, Douglas N.; Lee, Jeonghun J.
2014
Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
2014
On the consistency of the combinatorial codifferential. Zbl 1298.58003
Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur
2014
Spaces of finite element differential forms. Zbl 1290.58003
Arnold, Douglas N.
2013
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100
Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay
2012
The serendipity family of finite elements. Zbl 1218.65125
Arnold, Douglas N.; Awanou, Gerard
2011
Nefarious numbers. Zbl 1223.01042
Arnold, Douglas N.; Fowler, Kristine K.
2011
Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2010
Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2009
Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132
Arnold, Douglas N.; Rognes, Marie E.
2009
Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
2008
Möbius transformations revealed. Zbl 1200.30036
Arnold, Douglas N.; Rogness, Jonathan
2008
Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2007
Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396
Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella
2007
Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134
Arnold, Douglas N.; Tarfulea, Nicolae
2007
Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
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
2006
Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
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
2006
Quadrilateral $$H$$(div) finite elements. Zbl 1086.65105
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
2005
Rectangular mixed finite elements for elasticity. Zbl 1077.74044
Arnold, Douglas N.; Awanou, Gerard
2005
A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068
Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella
2005
Nonconforming mixed elements for elasticity. Zbl 1057.74036
Arnold, Douglas N.; Winther, Ragnar
2003
Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388
Arnold, Douglas N.; Winther, Ragnar
2003
Asymptotic estimates of hierarchical modeling. Zbl 1046.35024
Arnold, Douglas N.; Madureira, Alexandre L.
2003
Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella
2002
Mixed finite elements for elasticity. Zbl 1090.74051
Arnold, Douglas N.; Winther, Ragnar
2002
Approximation by quadrilateral finite elements. Zbl 0993.65125
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
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
2002
Differential complexes and numerical stability. Zbl 1023.65113
Arnold, Douglas N.
2002
Finite element approximation on quadrilateral meshes. Zbl 0999.76073
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia
2001
Multigrid in H(div) and H(curl). Zbl 0974.65113
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
2000
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
2000
Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116
Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc
2000
Numerical problems in general relativity. Zbl 0976.83002
Arnold, Douglas N.
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.
1999
Multigrid preconditioning in $$H(\text{div})$$ on non-convex polygons. Zbl 0922.65078
Arnold, D. N.; Falk, R. S.; Winther, R.
1998
Adaptive finite elements and colliding black holes. Zbl 0902.65080
Arnold, D. N.; Mukherjee, A.; Pouly, L.
1998
Preconditioning in H $$(\operatorname{div})$$ and applications. Zbl 0870.65112
Arnold, Douglas N.; Falk, Richard S.; Winther, R.
1997
Locking-free finite element methods for shells. Zbl 0854.65095
Arnold, Douglas N.; Brezzi, Franco
1997
Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
1997
Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068
Arnold, Douglas N.; Falk, Richard S.
1997
Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585
Arnold, Douglas N.; Liu, Xiaobo
1997
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027
Arnold, Douglas N.; Falk, Richard S.
1996
Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117
Arnold, Douglas N.; Liu, Xiaobo
1995
On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128
Arnold, Douglas N.
1994
Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058
Arnold, Douglas N.; Brezzi, Franco
1993
Innovative finite element methods for plates. Zbl 0757.73048
Arnold, Douglas N.
1991
Mixed finite element methods for elliptic problems. Zbl 0729.73198
Arnold, Douglas N.
1990
The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042
Arnold, Douglas N.; Falk, Richard S.
1990
A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040
Arnold, Douglas N.; Falk, Richard S.
1989
Coercivity of the single layer heat potential. Zbl 0672.65092
Arnold, Douglas N.; Noon, Patrick J.
1989
A new mixed formulation for elasticity. Zbl 0621.73102
Arnold, Douglas N.; Falk, Richard S.
1988
Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Zbl 0702.35208
Arnold, Douglas N.; Scott, L. Ridgway; Vogelius, Michael
1988
The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067
Cheng, R. S.-C.; Arnold, D. N.
1988
Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012
Arnold, Douglas N.; Falk, Richard S.
1987
Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078
Arnold, D. N.; Brezzi, F.
1985
The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077
Arnold, Douglas N.; Wendland, Wolfgang L.
1985
A stable finite element for the Stokes equations. Zbl 0593.76039
Arnold, D. N.; Brezzi, F.; Fortin, M.
1984
PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074
Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun.
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.
1984
On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069
Arnold, Douglas N.; Saranen, Jukka
1984
Finite element methods: Principles for their selection. Zbl 0513.73081
Arnold, D. N.; Babuška, Ivo; Osborn, J.
1984
On the asymptotic convergence of collocation methods. Zbl 0541.65075
Arnold, Douglas N.; Wendland, Wolfgang L.
1983
A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087
Arnold, Douglas N.
1983
An interior penalty finite element method with discontinuous elements. Zbl 0482.65060
Arnold, Douglas N.
1982
A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028
Arnold, Douglas N.; Winther, Ragnar
1982
Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092
Arnold, D. N.; Wendland, W. L.
1982
Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066
Arnold, Douglas N.
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
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.
1979
all top 5

### Cited by 3,912 Authors

 54 Cockburn, Bernardo 48 Gatica, Gabriel N. 38 Ye, Xiu 34 Zhang, Shangyou 32 Antonietti, Paola Francesca 32 Brezzi, Franco 32 Hughes, Thomas J. R. 31 Beirão da Veiga, Lourenço 30 Carstensen, Carsten 29 Sayas, Francisco-Javier 28 Hiptmair, Ralf 28 Xu, Jinchao 27 Arnold, Douglas Norman 27 Schötzau, Dominik 26 Bassi, Francesco 25 Houston, Paul 25 Marini, Luisa Donatella 24 Di Pietro, Daniele Antonio 24 Stenberg, Rolf 24 Wheeler, Mary Fanett 23 Chen, Zhangxin 23 Guzmán, Johnny 23 Lovadina, Carlo 23 Meddahi, Salim 23 Winther, Ragnar 22 Brenner, Susanne Cecelia 22 Franca, Leopoldo Luis Cabo Penna 22 Hu, Jun 22 Rivière, Beatrice M. 22 Ruiz-Baier, Ricardo 22 Schöberl, Joachim 22 Zhang, Zhimin 21 Xie, Xiaoping 20 He, Yinnian 20 Mu, Lin 19 Huang, Xuehai 19 Pani, Amiya Kumar 19 Park, Eun-Jae 19 Wang, Junping 19 Zikatanov, Ludmil T. 18 Crivellini, Andrea 18 Giani, Stefano 18 Marquez-Duran, Antonio M. 18 Perugia, Ilaria 18 Vohralík, Martin 18 Yotov, Ivan 17 Bazilevs, Yuri 17 Chen, Long 17 Huang, Yunqing 17 Loula, Abimael Fernando Dourado 16 Boffi, Daniele 16 Chen, Shaochun 16 Christiansen, Snorre Harald 16 Ern, Alexandre 16 Evans, John A. 16 Gudi, Thirupathi 16 Kanschat, Guido 16 Larson, Mats G. 16 Neilan, Michael 16 Qiu, Weifeng 16 Vassilevski, Panayot Spirov 15 Ainsworth, Mark 15 Scovazzi, Guglielmo 15 Shang, Yueqiang 15 Shi, Zhongci 15 Wohlmuth, Barbara I. 14 Botti, Lorenzo 14 Buffa, Annalisa 14 Dolejší, Vít 14 Han, Weimin 14 Oyarzúa, Ricardo 14 Russo, Alessandro 14 Schwab, Christoph 14 Wendland, Wolfgang L. 13 Colombo, Alessandro G. 13 Falk, Richard S. 13 Gerritsma, Marc I. 13 Hu, Kaibo 13 Hu, Xiaozhe 13 Karasözen, Bülent 13 Lamichhane, Bishnu Prasad 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 12 Auricchio, Ferdinando 12 Barrios, Tomás P. 12 Bustinza, Rommel A. 12 Calo, Victor Manuel 12 Chen, Jinru 12 Demkowicz, Leszek F. 12 Duan, Huoyuan 12 Durán, Ricardo G. 12 Ghidoni, Antonio 12 Kraus, Johannes K. 12 Lee, Jeonghun J. 12 Li, Jian ...and 3,812 more Authors
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### Cited in 245 Serials

 481 Computer Methods in Applied Mechanics and Engineering 297 Journal of Computational Physics 252 Journal of Scientific Computing 193 Numerische Mathematik 180 Journal of Computational and Applied Mathematics 177 Mathematics of Computation 171 Computers & Mathematics with Applications 114 Applied Numerical Mathematics 93 SIAM Journal on Scientific Computing 84 International Journal for Numerical Methods in Engineering 83 SIAM Journal on Numerical Analysis 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 39 Advances in Computational Mathematics 37 Calcolo 33 Computational Geosciences 31 Computational Methods in Applied Mathematics 27 Advances in Applied Mathematics and Mechanics 26 International Journal for Numerical Methods in Fluids 26 RAIRO. Modélisation Mathématique et Analyse Numérique 23 Science China. Mathematics 22 Comptes Rendus. Mathématique. Académie des Sciences, Paris 20 Journal of Numerical Mathematics 19 Journal of Mathematical Analysis and Applications 19 Mathematics and Computers in Simulation 19 Applied Mathematics Letters 19 Numerical Algorithms 19 Numerical Linear Algebra with Applications 19 International Journal of Numerical Analysis and Modeling 18 BIT 18 Communications in Numerical Methods in Engineering 17 Journal of Integral Equations and Applications 16 Japan Journal of Industrial and Applied Mathematics 16 Engineering Analysis with Boundary Elements 16 Foundations of Computational Mathematics 16 Communications in Computational Physics 15 Applicable Analysis 15 Applied Mathematical Modelling 15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 13 Numerical Functional Analysis and Optimization 13 International Journal of Computer Mathematics 13 Communications on Applied Mathematics and Computation 12 Mathematical Methods in the Applied Sciences 12 Computational and Applied Mathematics 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 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 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 4 East Asian Journal on Applied Mathematics 3 Inverse Problems 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 ACM Transactions on Graphics 3 SIAM Journal on Mathematical Analysis 3 Bulletin of the American Mathematical Society. New Series 3 Journal of Nonlinear Science ...and 145 more Serials
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### Cited in 51 Fields

 2,914 Numerical analysis (65-XX) 1,374 Partial differential equations (35-XX) 1,154 Fluid mechanics (76-XX) 928 Mechanics of deformable solids (74-XX) 176 Optics, electromagnetic theory (78-XX) 85 Calculus of variations and optimal control; optimization (49-XX) 78 Global analysis, analysis on manifolds (58-XX) 73 Integral equations (45-XX) 63 Geophysics (86-XX) 57 Statistical mechanics, structure of matter (82-XX) 49 Classical thermodynamics, heat transfer (80-XX) 45 Biology and other natural sciences (92-XX) 35 Operator theory (47-XX) 31 Computer science (68-XX) 30 Approximations and expansions (41-XX) 26 Potential theory (31-XX) 26 Ordinary differential equations (34-XX) 20 Differential geometry (53-XX) 18 Dynamical systems and ergodic theory (37-XX) 18 Functional analysis (46-XX) 17 Quantum theory (81-XX) 15 Probability theory and stochastic processes (60-XX) 15 Systems theory; control (93-XX) 11 Real functions (26-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Operations research, mathematical programming (90-XX) 9 Statistics (62-XX) 9 Mechanics of particles and systems (70-XX) 9 Relativity and gravitational theory (83-XX) 8 Functions of a complex variable (30-XX) 7 General and overarching topics; collections (00-XX) 7 Harmonic analysis on Euclidean spaces (42-XX) 7 Information and communication theory, circuits (94-XX) 6 Algebraic topology (55-XX) 5 History and biography (01-XX) 5 Algebraic geometry (14-XX) 5 Convex and discrete geometry (52-XX) 4 Combinatorics (05-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 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)

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