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Arnold, Douglas Norman

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Author ID: arnold.douglas-n Recent zbMATH articles by "Arnold, Douglas Norman"
Published as: Arnold, Douglas N.; Arnold, D. N.; Arnold, Douglas
Homepage: http://www-users.math.umn.edu/~arnold/
External Links: MGP · ORCID · Wikidata · dblp · GND · IdRef
Documents Indexed: 88 Publications since 1979, including 2 Books
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

Publications by Year

Citations contained in zbMATH Open

80 Publications have been cited 5,209 times in 3,388 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.
567
1982
A stable finite element for the Stokes equations. Zbl 0593.76039
Arnold, D. N.; Brezzi, F.; Fortin, M.
369
1984
Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078
Arnold, D. N.; Brezzi, F.
301
1985
Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
285
2006
Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
180
2010
PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074
Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun.
168
1984
Mixed finite elements for elasticity. Zbl 1090.74051
Arnold, Douglas N.; Winther, Ragnar
163
2002
A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040
Arnold, Douglas N.; Falk, Richard S.
130
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.
123
1984
Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
112
2007
Approximation by quadrilateral finite elements. Zbl 0993.65125
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
92
2002
Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
82
2005
Multigrid in H(div) and H(curl). Zbl 0974.65113
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
78
2000
Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
77
2008
Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066
Arnold, Douglas N.
75
1981
On the asymptotic convergence of collocation methods. Zbl 0541.65075
Arnold, Douglas N.; Wendland, Wolfgang L.
68
1983
Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112
Arnold, Douglas N.; Falk, Richard S.; Winther, R.
68
1997
The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077
Arnold, Douglas N.; Wendland, Wolfgang L.
65
1985
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
64
2000
Mixed finite element methods for elliptic problems. Zbl 0729.73198
Arnold, Douglas N.
54
1990
Rectangular mixed finite elements for elasticity. Zbl 1077.74044
Arnold, Douglas N.; Awanou, Gerard
48
2005
Nonconforming mixed elements for elasticity. Zbl 1057.74036
Arnold, Douglas N.; Winther, Ragnar
48
2003
Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116
Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc
47
2000
A new mixed formulation for elasticity. Zbl 0621.73102
Arnold, Douglas N.; Falk, Richard S.
46
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
45
1988
The serendipity family of finite elements. Zbl 1218.65125
Arnold, Douglas N.; Awanou, Gerard
43
2011
The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042
Arnold, Douglas N.; Falk, Richard S.
42
1990
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027
Arnold, Douglas N.; Falk, Richard S.
36
1996
A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068
Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella
32
2005
Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
31
2009
A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087
Arnold, Douglas N.
28
1983
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
28
1981
Differential complexes and stability of finite element methods. I: The de Rham complex. Zbl 1119.65398
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
28
2006
Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396
Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella
26
2007
Locking-free finite element methods for shells. Zbl 0854.65095
Arnold, Douglas N.; Brezzi, Franco
25
1997
Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117
Arnold, Douglas N.; Liu, Xiaobo
24
1995
Finite element differential forms on cubical meshes. Zbl 1297.65142
Arnold, Douglas N.; Awanou, Gerard
24
2014
Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058
Arnold, Douglas N.; Brezzi, Franco
22
1993
On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069
Arnold, Douglas N.; Saranen, Jukka
21
1984
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
21
2002
Coercivity of the single layer heat potential. Zbl 0672.65092
Arnold, Douglas N.; Noon, Patrick J.
20
1989
Differential complexes and numerical stability. Zbl 1023.65113
Arnold, Douglas N.
20
2002
Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012
Arnold, Douglas N.; Falk, Richard S.
20
1987
Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
20
1997
Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193
Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca
19
2015
Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
18
2006
Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068
Arnold, Douglas N.; Falk, Richard S.
15
1997
Derivation and justification of plate models by variational methods. Zbl 0958.74033
Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L.
14
1999
Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033
Arnold, Douglas N.; Lee, Jeonghun J.
13
2014
Spaces of finite element differential forms. Zbl 1290.58003
Arnold, Douglas N.
13
2013
Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096
Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng
12
2015
Finite element approximation on quadrilateral meshes. Zbl 0999.76073
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia
12
2001
Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
12
2014
Innovative finite element methods for plates. Zbl 0757.73048
Arnold, Douglas N.
10
1991
A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028
Arnold, Douglas N.; Winther, Ragnar
10
1982
Finite element methods: Principles for their selection. Zbl 0513.73081
Arnold, D. N.; Babuška, Ivo; Osborn, J.
9
1984
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
Arnold, Douglas N. (ed.); Bochev, Pavel B. (ed.); Lehoucq, Richard B. (ed.); Nicolaides, Roy A. (ed.); Shashkov, Mikhail (ed.)
9
2006
Finite element exterior calculus. Zbl 07045589
Arnold, Douglas N.
9
2018
Localization of eigenfunctions via an effective potential. Zbl 1432.35061
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
8
2019
Computing spectra without solving eigenvalue problems. Zbl 1420.81009
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
8
2019
Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388
Arnold, Douglas N.; Winther, Ragnar
8
2003
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100
Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay
8
2012
Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094
Arnold, D. N.; Douglas, Jim jun.
7
1979
Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092
Arnold, D. N.; Wendland, W. L.
6
1982
The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067
Cheng, R. S.-C.; Arnold, D. N.
6
1988
Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078
Arnold, D. N.; Falk, R. S.; Winther, R.
6
1998
On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128
Arnold, Douglas N.
6
1994
Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585
Arnold, Douglas N.; Liu, Xiaobo
6
1997
Asymptotic estimates of hierarchical modeling. Zbl 1046.35024
Arnold, Douglas N.; Madureira, Alexandre L.
5
2003
Finite element exterior calculus for parabolic problems. Zbl 1362.65100
Arnold, Douglas N.; Chen, Hongtao
3
2017
Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134
Arnold, Douglas N.; Tarfulea, Nicolae
2
2007
Möbius transformations revealed. Zbl 1200.30036
Arnold, Douglas N.; Rogness, Jonathan
2
2008
Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132
Arnold, Douglas N.; Rognes, Marie E.
2
2009
On the consistency of the combinatorial codifferential. Zbl 1298.58003
Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur
2
2014
The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182
Arnold, Douglas N.; Walker, Shawn W.
1
2020
Numerical problems in general relativity. Zbl 0976.83002
Arnold, Douglas N.
1
2000
Adaptive finite elements and colliding black holes. Zbl 0902.65080
Arnold, D. N.; Mukherjee, A.; Pouly, L.
1
1998
Nefarious numbers. Zbl 1223.01042
Arnold, Douglas N.; Fowler, Kristine K.
1
2011
Finite element exterior calculus with lower-order terms. Zbl 1364.65236
Arnold, Douglas N.; Li, Lizao
1
2017
The Hellan-Herrmann-Johnson method with curved elements. Zbl 1451.65182
Arnold, Douglas N.; Walker, Shawn W.
1
2020
Localization of eigenfunctions via an effective potential. Zbl 1432.35061
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
8
2019
Computing spectra without solving eigenvalue problems. Zbl 1420.81009
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana
8
2019
Finite element exterior calculus. Zbl 07045589
Arnold, Douglas N.
9
2018
Finite element exterior calculus for parabolic problems. Zbl 1362.65100
Arnold, Douglas N.; Chen, Hongtao
3
2017
Finite element exterior calculus with lower-order terms. Zbl 1364.65236
Arnold, Douglas N.; Li, Lizao
1
2017
Finite element differential forms on curvilinear cubic meshes and their approximation properties. Zbl 1308.65193
Arnold, Douglas N.; Boffi, Daniele; Bonizzoni, Francesca
19
2015
Mixed finite elements for elasticity on quadrilateral meshes. Zbl 1320.74096
Arnold, Douglas N.; Awanou, Gerard; Qiu, Weifeng
12
2015
Finite element differential forms on cubical meshes. Zbl 1297.65142
Arnold, Douglas N.; Awanou, Gerard
24
2014
Mixed methods for elastodynamics with weak symmetry. Zbl 1309.74033
Arnold, Douglas N.; Lee, Jeonghun J.
13
2014
Nonconforming tetrahedral mixed finite elements for elasticity. Zbl 1433.74097
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
12
2014
On the consistency of the combinatorial codifferential. Zbl 1298.58003
Arnold, Douglas N.; Falk, Richard S.; Guzmán, Johnny; Tsogtgerel, Gantumur
2
2014
Spaces of finite element differential forms. Zbl 1290.58003
Arnold, Douglas N.
13
2013
Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Zbl 1260.65100
Arnold, Douglas N.; Falk, Richard S.; Gopalakrishnan, Jay
8
2012
The serendipity family of finite elements. Zbl 1218.65125
Arnold, Douglas N.; Awanou, Gerard
43
2011
Nefarious numbers. Zbl 1223.01042
Arnold, Douglas N.; Fowler, Kristine K.
1
2011
Finite element exterior calculus: From Hodge theory to numerical stability. Zbl 1207.65134
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
180
2010
Geometric decompositions and local bases for spaces of finite element differential forms. Zbl 1227.65091
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
31
2009
Stability of Lagrange elements for the mixed Laplacian. Zbl 1181.65132
Arnold, Douglas N.; Rognes, Marie E.
2
2009
Finite elements for symmetric tensors in three dimensions. Zbl 1285.74013
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
77
2008
Möbius transformations revealed. Zbl 1200.30036
Arnold, Douglas N.; Rogness, Jonathan
2
2008
Mixed finite element methods for linear elasticity with weakly imposed symmetry. Zbl 1118.74046
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
112
2007
Locking-free Reissner-Mindlin elements without reduced integration. Zbl 1173.74396
Arnold, Douglas N.; Brezzi, Franco; Falk, Richard S.; Marini, L. Donatella
26
2007
Boundary conditions for the Einstein-Christoffel formulation of Einstein’s equations. Zbl 1115.35134
Arnold, Douglas N.; Tarfulea, Nicolae
2
2007
Finite element exterior calculus, homological techniques, and applications. Zbl 1185.65204
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
285
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
28
2006
Differential complexes and stability of finite element methods. II: The elasticity complex. Zbl 1119.65399
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
18
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
Arnold, Douglas N.; Bochev, Pavel B.; Lehoucq, Richard B.; Nicolaides, Roy A.; Shashkov, Mikhail
9
2006
Quadrilateral \(H\)(div) finite elements. Zbl 1086.65105
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
82
2005
Rectangular mixed finite elements for elasticity. Zbl 1077.74044
Arnold, Douglas N.; Awanou, Gerard
48
2005
A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. Zbl 1065.74068
Arnold, Douglas N.; Brezzi, Franco; Marini, L. Donatella
32
2005
Nonconforming mixed elements for elasticity. Zbl 1057.74036
Arnold, Douglas N.; Winther, Ragnar
48
2003
Mixed finite elements for elasticity in the stress-displacement formulation. Zbl 1138.74388
Arnold, Douglas N.; Winther, Ragnar
8
2003
Asymptotic estimates of hierarchical modeling. Zbl 1046.35024
Arnold, Douglas N.; Madureira, Alexandre L.
5
2003
Unified analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1008.65080
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, L. Donatella
2002
Mixed finite elements for elasticity. Zbl 1090.74051
Arnold, Douglas N.; Winther, Ragnar
163
2002
Approximation by quadrilateral finite elements. Zbl 0993.65125
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
92
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
21
2002
Differential complexes and numerical stability. Zbl 1023.65113
Arnold, Douglas N.
20
2002
Finite element approximation on quadrilateral meshes. Zbl 0999.76073
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.; Gastaldi, Lucia
12
2001
Multigrid in H(div) and H(curl). Zbl 0974.65113
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
78
2000
Discontinuous Galerkin methods for elliptic problems. Zbl 0948.65127
Arnold, Douglas N.; Brezzi, Franco; Cockburn, Bernardo; Marini, Donatella
64
2000
Locally adapted tetrahedral meshes using bisection. Zbl 0973.65116
Arnold, Douglas N.; Mukherjee, Arup; Pouly, Luc
47
2000
Numerical problems in general relativity. Zbl 0976.83002
Arnold, Douglas N.
1
2000
Derivation and justification of plate models by variational methods. Zbl 0958.74033
Alessandrini, Stephen M.; Arnold, Douglas N.; Falk, Richard S.; Madureira, Alexandre L.
14
1999
Multigrid preconditioning in \(H(\text{div})\) on non-convex polygons. Zbl 0922.65078
Arnold, D. N.; Falk, R. S.; Winther, R.
6
1998
Adaptive finite elements and colliding black holes. Zbl 0902.65080
Arnold, D. N.; Mukherjee, A.; Pouly, L.
1
1998
Preconditioning in H \((\operatorname{div})\) and applications. Zbl 0870.65112
Arnold, Douglas N.; Falk, Richard S.; Winther, R.
68
1997
Locking-free finite element methods for shells. Zbl 0854.65095
Arnold, Douglas N.; Brezzi, Franco
25
1997
Preconditioning discrete approximations of the Reissner-Mindlin plate model. Zbl 0877.73060
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
20
1997
Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Zbl 0869.73068
Arnold, Douglas N.; Falk, Richard S.
15
1997
Interior estimates for a low-order finite element method for the Reissner-Mindlin plate model. Zbl 1066.74585
Arnold, Douglas N.; Liu, Xiaobo
6
1997
Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. Zbl 0846.73027
Arnold, Douglas N.; Falk, Richard S.
36
1996
Local error estimates for finite element discretizations of the Stokes equations. Zbl 0832.65117
Arnold, Douglas N.; Liu, Xiaobo
24
1995
On nonconforming linear-constant elements for some variants of the Stokes equations. Zbl 0923.76128
Arnold, Douglas N.
6
1994
Some new elements for the Reissner-Mindlin plate model. Zbl 0817.73058
Arnold, Douglas N.; Brezzi, Franco
22
1993
Innovative finite element methods for plates. Zbl 0757.73048
Arnold, Douglas N.
10
1991
Mixed finite element methods for elliptic problems. Zbl 0729.73198
Arnold, Douglas N.
54
1990
The boundary layer for the Reissner-Mindlin plate model. Zbl 0698.73042
Arnold, Douglas N.; Falk, Richard S.
42
1990
A uniformly accurate finite element method for the Reissner-Mindlin plate. Zbl 0696.73040
Arnold, Douglas N.; Falk, Richard S.
130
1989
Coercivity of the single layer heat potential. Zbl 0672.65092
Arnold, Douglas N.; Noon, Patrick J.
20
1989
A new mixed formulation for elasticity. Zbl 0621.73102
Arnold, Douglas N.; Falk, Richard S.
46
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
45
1988
The delta-trigonometric method using the single-layer potential representation. Zbl 0689.65067
Cheng, R. S.-C.; Arnold, D. N.
6
1988
Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Zbl 0618.73012
Arnold, Douglas N.; Falk, Richard S.
20
1987
Mixed and nonconforming finite element methods: Implementation, postprocessing and error estimates. Zbl 0567.65078
Arnold, D. N.; Brezzi, F.
301
1985
The convergence of spline collocation for strongly elliptic equations on curves. Zbl 0592.65077
Arnold, Douglas N.; Wendland, Wolfgang L.
65
1985
A stable finite element for the Stokes equations. Zbl 0593.76039
Arnold, D. N.; Brezzi, F.; Fortin, M.
369
1984
PEERS: A new mixed finite element for plane elasticity. Zbl 0633.73074
Arnold, Douglas N.; Brezzi, Franco; Douglas, Jim jun.
168
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.
123
1984
On the asymptotic convergence of spline collocation methods for partial differential equations. Zbl 0542.65069
Arnold, Douglas N.; Saranen, Jukka
21
1984
Finite element methods: Principles for their selection. Zbl 0513.73081
Arnold, D. N.; Babuška, Ivo; Osborn, J.
9
1984
On the asymptotic convergence of collocation methods. Zbl 0541.65075
Arnold, Douglas N.; Wendland, Wolfgang L.
68
1983
A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Zbl 0543.65087
Arnold, Douglas N.
28
1983
An interior penalty finite element method with discontinuous elements. Zbl 0482.65060
Arnold, Douglas N.
567
1982
A superconvergent finite element method for the Korteweg-de Vries equation. Zbl 0487.76028
Arnold, Douglas N.; Winther, Ragnar
10
1982
Collocation versus Galerkin procedures for boundary integral methods. Zbl 0521.65092
Arnold, D. N.; Wendland, W. L.
6
1982
Discretization by finite elements of a model parameter dependent problem. Zbl 0446.73066
Arnold, Douglas N.
75
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
28
1981
Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Zbl 0435.65094
Arnold, D. N.; Douglas, Jim jun.
7
1979
all top 5

Cited by 3,577 Authors

52 Cockburn, Bernardo
45 Gatica, Gabriel N.
35 Ye, Xiu
32 Brezzi, Franco
31 Beirão da Veiga, Lourenço
30 Hughes, Thomas J. R.
30 Zhang, Shangyou
29 Sayas, Francisco-Javier
28 Antonietti, Paola Francesca
28 Carstensen, Carsten
27 Schötzau, Dominik
25 Arnold, Douglas Norman
25 Bassi, Francesco
25 Hiptmair, Ralf
25 Houston, Paul
25 Marini, Luisa Donatella
24 Stenberg, Rolf
24 Wheeler, Mary Fanett
24 Xu, Jinchao
23 Chen, Zhangxin
23 Winther, Ragnar
22 Brenner, Susanne Cecelia
22 Franca, Leopoldo Luis Cabo Penna
22 Lovadina, Carlo
21 Guzmán, Johnny
21 Rivière, Beatrice M.
21 Zhang, Zhimin
20 Di Pietro, Daniele Antonio
20 Meddahi, Salim
19 Mu, Lin
19 Ruiz-Baier, Ricardo
19 Schöberl, Joachim
19 Xie, Xiaoping
18 Giani, Stefano
18 Hu, Jun
18 Huang, Xuehai
18 Pani, Amiya Kumar
18 Perugia, Ilaria
18 Wang, Junping
18 Zikatanov, Ludmil T.
17 Bazilevs, Yuri
17 Loula, Abimael Fernando Dourado
17 Park, Eun-Jae
16 Chen, Long
16 Chen, Shaochun
16 Christiansen, Snorre Harald
16 He, Yinnian
16 Larson, Mats G.
16 Marquez-Duran, Antonio M.
16 Neilan, Michael
16 Vassilevski, Panayot Spirov
16 Vohralík, Martin
16 Yotov, Ivan
15 Boffi, Daniele
15 Buffa, Annalisa
15 Crivellini, Andrea
15 Evans, John A.
15 Gudi, Thirupathi
15 Huang, Yunqing
15 Kanschat, Guido
15 Scovazzi, Guglielmo
15 Shi, Zhongci
15 Wohlmuth, Barbara I.
14 Ainsworth, Mark
14 Dolejší, Vít
14 Oyarzúa, Ricardo
14 Qiu, Weifeng
14 Russo, Alessandro
14 Schwab, Christoph
14 Wendland, Wolfgang L.
13 Ern, Alexandre
13 Falk, Richard S.
13 Han, Weimin
13 Karasözen, Bülent
13 Lamichhane, Bishnu Prasad
13 Sacco, Riccardo
13 Shang, Yueqiang
13 Shu, Chi-Wang
13 Wihler, Thomas Pascal
12 Auricchio, Ferdinando
12 Chen, Jinru
12 Demkowicz, Leszek F.
12 Duan, Huoyuan
12 Durán, Ricardo G.
12 Li, Jian
12 Liu, Gui-Rong
12 Nguyen, Ngoc Cuong
12 Nordbotten, Jan Martin
12 Reddy, B. Dayanand
12 Uzunca, Murat
12 van der Vegt, Jaap J. W.
12 Wu, Haijun
11 Bi, Chunjia
11 Bochev, Pavel B.
11 Calo, Victor Manuel
11 Codina, Ramon
11 Gillette, Andrew
11 Hu, Xiaozhe
11 Kraus, Johannes K.
11 Kwak, Do Young
...and 3,477 more Authors
all top 5

Cited in 228 Serials

453 Computer Methods in Applied Mechanics and Engineering
262 Journal of Computational Physics
231 Journal of Scientific Computing
187 Numerische Mathematik
173 Mathematics of Computation
173 Journal of Computational and Applied Mathematics
154 Computers & Mathematics with Applications
112 Applied Numerical Mathematics
84 International Journal for Numerical Methods in Engineering
81 SIAM Journal on Scientific Computing
80 SIAM Journal on Numerical Analysis
79 Numerical Methods for Partial Differential Equations
69 Applied Mathematics and Computation
67 Computers and Fluids
67 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences
50 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
47 Computational Mechanics
35 Calcolo
33 Advances in Computational Mathematics
31 Computational Geosciences
26 International Journal for Numerical Methods in Fluids
26 RAIRO. Modélisation Mathématique et Analyse Numérique
25 Advances in Applied Mathematics and Mechanics
23 Computational Methods in Applied Mathematics
22 Comptes Rendus. Mathématique. Académie des Sciences, Paris
20 Science China. Mathematics
19 Journal of Mathematical Analysis and Applications
19 Numerical Linear Algebra with Applications
18 Applied Mathematics Letters
18 Communications in Numerical Methods in Engineering
17 BIT
17 Journal of Numerical Mathematics
16 Journal of Integral Equations and Applications
16 Japan Journal of Industrial and Applied Mathematics
15 Mathematics and Computers in Simulation
15 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics
14 Engineering Analysis with Boundary Elements
14 Foundations of Computational Mathematics
13 Applicable Analysis
13 Numerical Algorithms
12 Mathematical Methods in the Applied Sciences
12 Numerical Functional Analysis and Optimization
11 Applied Mathematical Modelling
11 International Journal of Computational Methods
10 Computing
10 Applications of Mathematics
10 Archives of Computational Methods in Engineering
10 SMAI Journal of Computational Mathematics
8 ETNA. Electronic Transactions on Numerical Analysis
7 Acta Mechanica
7 Integral Equations and Operator Theory
7 Computational and Applied Mathematics
7 Mathematical Problems in Engineering
7 Abstract and Applied Analysis
7 European Journal of Mechanics. A. Solids
6 International Journal of Computer Mathematics
6 International Journal of Computational Fluid Dynamics
6 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik
6 Journal of Applied Mathematics and Computing
6 International Journal of Numerical Analysis and Modeling
5 Journal of Elasticity
5 SIAM Review
5 Journal of Mathematical Sciences (New York)
5 Computing and Visualization in Science
5 Discrete and Continuous Dynamical Systems. Series B
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 Journal of Mathematical Physics
4 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
4 Applied Mathematics and Mechanics. (English Edition)
4 Computer Aided Geometric Design
4 International Journal of Numerical Methods for Heat & Fluid Flow
4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations
4 Engineering Computations
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 the Mechanics and Physics of Solids
3 ZAMP. Zeitschrift für angewandte Mathematik und Physik
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 Communications in Partial Differential Equations
3 Bulletin of the American Mathematical Society. New Series
3 Journal of Nonlinear Science
3 Journal of Inequalities and Applications
3 Communications in Nonlinear Science and Numerical Simulation
3 Advances in Difference Equations
3 Oberwolfach Reports
3 Acta Mechanica Sinica
3 Frontiers of Mathematics in China
3 Advances in Numerical Analysis
...and 128 more Serials
all top 5

Cited in 51 Fields

2,639 Numerical analysis (65-XX)
1,244 Partial differential equations (35-XX)
1,007 Fluid mechanics (76-XX)
864 Mechanics of deformable solids (74-XX)
162 Optics, electromagnetic theory (78-XX)
75 Calculus of variations and optimal control; optimization (49-XX)
67 Integral equations (45-XX)
66 Global analysis, analysis on manifolds (58-XX)
54 Geophysics (86-XX)
49 Statistical mechanics, structure of matter (82-XX)
46 Classical thermodynamics, heat transfer (80-XX)
42 Biology and other natural sciences (92-XX)
33 Operator theory (47-XX)
26 Approximations and expansions (41-XX)
26 Computer science (68-XX)
25 Ordinary differential equations (34-XX)
22 Potential theory (31-XX)
18 Functional analysis (46-XX)
16 Dynamical systems and ergodic theory (37-XX)
16 Differential geometry (53-XX)
15 Quantum theory (81-XX)
13 Probability theory and stochastic processes (60-XX)
11 Systems theory; control (93-XX)
8 Linear and multilinear algebra; matrix theory (15-XX)
8 Real functions (26-XX)
7 Functions of a complex variable (30-XX)
7 Statistics (62-XX)
7 Mechanics of particles and systems (70-XX)
7 Relativity and gravitational theory (83-XX)
7 Operations research, mathematical programming (90-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)
5 History and biography (01-XX)
5 Algebraic geometry (14-XX)
5 Convex and discrete geometry (52-XX)
5 Algebraic topology (55-XX)
4 Combinatorics (05-XX)
4 Difference and functional equations (39-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)
1  (73-XX)

Citations by Year

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