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## Thomée, Vidar

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 Author ID: thomee.vidar Published as: Thomée, Vidar; Thomee, Vidar; Thomée, V.; Thomee, V. Homepage: http://www.math.chalmers.se/~thomee/ External Links: MGP · Wikidata · dblp · GND · IdRef
 Documents Indexed: 154 Publications since 1955, including 9 Books
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#### Co-Authors

 53 single-authored 22 Wahlbin, Lars B. 13 Larsson, Stig 10 Bramble, James H. 9 Crouzeix, Michel 8 McLean, William 7 Brenner, Philip 6 Chatzipantelidis, Panagiotis 6 Sloan, Ian Hugh 5 Johnson, Claes G. L. 5 Lazarov, Raytcho D. 4 Bakaev, Nikolai Yu. 4 Schatz, Alfred H. 4 Zhang, Naiying 3 Chen, Chuanmiao 3 Huang, Mingyou 3 Vasudeva Murthy, A. S. 2 Eriksson, Kenneth 2 Nie, Yiyong 2 Pani, Amiya Kumar 2 Sheen, Dongwoo 1 Akrivis, Georgios D. 1 Arnold, Douglas Norman 1 Baker, Garth A. 1 Björck, Göran 1 Chen, Chuan-omia 1 Douglas, Jim jun. 1 Dupont, Todd F. 1 Horváth, Zoltán 1 Hubbard, B. E. 1 Jin, Bangti 1 Keller, Herbert Bishop 1 Kellogg, Bruce 1 Kreiss, Heinz-Otto 1 Le Roux, Marie-Noelle 1 Lin, Yanping 1 Löfström, Jörgen 1 Loula, Abimael Fernando Dourado 1 Lubich, Christian 1 Murad, Márcio Arab 1 Pasciak, Joseph E. 1 Peetre, Jaak 1 Piskarëv, S. I. 1 Sammon, Peter H. 1 Schatz, Albert H. 1 Wendland, Wolfgang L. 1 Wendroff, Burton 1 Westergren, Bertil 1 Widlund, Olof B. 1 Xu, Jinchao 1 Zhou, Zhi
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#### Serials

 29 Mathematics of Computation 15 SIAM Journal on Numerical Analysis 8 Mathematica Scandinavica 7 Computational Methods in Applied Mathematics 5 IMA Journal of Numerical Analysis 5 Numerische Mathematik 4 Communications on Pure and Applied Mathematics 4 BIT 3 Archive for Rational Mechanics and Analysis 2 Journal of the Australian Mathematical Society, Series B 2 Calcolo 2 Journal of Computational and Applied Mathematics 2 RAIRO. Analyse Numérique 2 Journal of Computational Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Numerical Methods for Partial Differential Equations 2 Journal of Integral Equations and Applications 2 Journal of the Society for Industrial & Applied Mathematics 2 Lecture Notes in Mathematics 2 Texts in Applied Mathematics 2 Revue Française d’Automatique, Informatique, Recherche Opérationnelle. Série Rouge 1 Bulletin of the Australian Mathematical Society 1 Journal of the Institute of Mathematics and its Applications 1 Mathematical Methods in the Applied Sciences 1 Arkiv för Matematik 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Journal of Differential Equations 1 Numerical Functional Analysis and Optimization 1 Journal of Integral Equations 1 Natural Science Journal of Xiangtan University 1 Asymptotic Analysis 1 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 1 SIAM Review 1 East-West Journal of Numerical Mathematics 1 European Series in Applied and Industrial Mathematics (ESAIM): Proceedings 1 The ANZIAM Journal 1 International Journal of Numerical Analysis and Modeling 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 BIT. Nordisk Tidskrift for Informationsbehandling 1 DMV Seminar 1 Springer Series in Computational Mathematics
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#### Fields

 129 Numerical analysis (65-XX) 81 Partial differential equations (35-XX) 22 Integral equations (45-XX) 7 Ordinary differential equations (34-XX) 6 Operator theory (47-XX) 5 Integral transforms, operational calculus (44-XX) 3 Approximations and expansions (41-XX) 2 History and biography (01-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Functional analysis (46-XX) 1 Fluid mechanics (76-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Geophysics (86-XX)

#### Citations contained in zbMATH Open

134 Publications have been cited 3,561 times in 2,365 Documents Cited by Year
Galerkin finite element methods for parabolic problems. 2nd revised and expanded ed. Zbl 1105.65102
Thomée, Vidar
2006
Galerkin finite element methods for parabolic problems. Zbl 0884.65097
Thomée, Vidar
1997
Galerkin finite element methods for parabolic problems. Zbl 0528.65052
Thomee, Vidar
1984
Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term. Zbl 0852.65138
Lubich, Ch.; Sloan, I. H.; Thomée, V.
1996
The stability in $$L_ p$$ and $$W^ 1_ p$$ of the $$L_ 2$$-projection onto finite element function spaces. Zbl 0637.41034
Crouzeix, M.; Thomée, V.
1987
Error estimates for some mixed finite element methods for parabolic type problems. Zbl 0476.65074
Johnson, Claes; Thomee, Vidar
1981
Numerical solution of an evolution equation with a positive-type memory term. Zbl 0791.65105
McLean, W.; Thomée, V.
1993
Time discretization of parabolic problems by the discontinuous Galerkin method. Zbl 0589.65070
Eriksson, Kenneth; Johnson, Claes; Thomée, Vidar
1985
Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations. Zbl 0728.65117
Lin, Yanping; Thomée, Vidar; Wahlbin, Lars B.
1991
Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. Zbl 1067.65092
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2004
Time discretization of an integro-differential equation of parabolic type. Zbl 0608.65096
Sloan, I. H.; Thomée, V.
1986
On rational approximations of semigroups. Zbl 0413.41011
Brenner, Philip; Thomee, Vidar
1979
Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations. Zbl 0364.65084
Bramble, J. H.; Schatz, A. H.; Thomee, V.; Wahlbin, L. B.
1977
Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method. Zbl 0896.65090
Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1998
A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature. Zbl 1022.65108
Sheen, Dongwoo; Sloan, Ian H.; Thomée, Vidar
2003
Besov spaces and applications to difference methods for initial value problems. Zbl 0294.35002
Brenner, Philip; Thomee, Vidar; Wahlbin, Lars B.
1975
Asymptotic behavior of semidiscrete finite element approximations of Biot’s consolidation problem. Zbl 0854.76053
Murad, Márcio A.; Thomée, Vidar; Loula, Abimael F. D.
1996
Error estimates for semidiscrete finite element methods for parabolic integro-differential equations. Zbl 0673.65099
Thomée, Vidar; Zhang, Nai-Ying
1989
The stability of rational approximations of analytic semigroups. Zbl 0783.65050
Crouzeix, M.; Larsson, S.; Piskarev, S.; Thomée, V.
1993
Numerical solution via Laplace transforms of a fractional order evolution equation. Zbl 1195.65122
McLean, William; Thomée, Vidar
2010
A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature. Zbl 0936.65109
Sheen, Dongwoo; Sloan, Ian H.; Thomée, Vidar
2000
High order local approximations to derivatives in the finite element method. Zbl 0367.65055
Thomee, Vidar
1977
Discretization with variable time steps of an evolution equation with a positive-type memory term. Zbl 0858.65143
McLean, W.; Thomée, V.; Wahlbin, L. B.
1996
Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel. Zbl 0766.65120
Chen, C.; Thomée, V.; Wahlbin, L. B.
1992
Numerical methods for hyperbolic and parabolic integro-differential equations. Zbl 0764.65086
Pani, A. K.; Thomée, V.; Wahlbin, L. B.
1992
Partial differential equations with numerical methods. Zbl 1025.65002
2003
Single step methods for inhomogeneous linear differential equations in Banach space. Zbl 0477.65040
Brenner, Philip; Crouzeix, Michel; Thomee, Vidar
1982
Time discretization of an evolution equation via Laplace transforms. Zbl 1068.65146
McLean, William; Thomée, Vidar
2004
Convergence estimates for Galerkin methods for variable coefficient initial value problems. Zbl 0292.65052
Thomee, Vidar; Wendroff, Burton
1974
Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation. Zbl 1416.65381
McLean, William; Thomée, Vidar
2010
An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem. Zbl 0701.65063
Johnson, Claes; Nie, Yi-Yong; Thomée, Vidar
1990
Maximum norm stability and error estimates in parabolic finite element equations. Zbl 0414.65066
Schatz, A. H.; Thomee, V.; Wahlbin, L. B.
1980
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
Galerkin methods for singular boundary value problems in one space dimension. Zbl 0546.65055
Eriksson, Kenneth; Thomée, Vidar
1984
On Galerkin methods in semilinear parabolic problems. Zbl 0307.35007
Thomee, Vidar; Wahlbin, Lars
1975
Finite-element methods for a strongly damped wave equation. Zbl 0718.65070
Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1991
Stability theory for partial difference operators. Zbl 0176.09101
Thomee, V.
1969
Smoothing of initial data and rates of convergence for parabolic difference equations. Zbl 0188.41001
Kreiss, H. O.; Thomee, V.; Widlund, O.
1970
Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Zbl 0454.65077
Thomee, Vidar
1980
Projection methods for Dirichlet’s problem in approximating polygonal domains with boundary-value corrections. Zbl 0279.65094
Bramble, James H.; Dupont, Todd; Thomee, Vidar
1972
Elliptic difference equations and interior regularity. Zbl 0159.38204
Thomee, V.; Westergren, B.
1968
Single step Galerkin approximations for parabolic problems. Zbl 0378.65061
Baker, Garth A.; Bramble, James H.; Thomee, Vidar
1977
Time discretization via Laplace transformation of an integro-differential equation of parabolic type. Zbl 1097.65131
McLean, William; Sloan, Ian H.; Thomée, Vidar
2006
Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations. Zbl 0932.65103
Schatz, A. H.; Thomée, V.; Wahlbin, L. B.
1998
Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem. Zbl 0678.65079
Thomée, Vidar; Xu, Jin-Chao; Zhang, Nai-Ying
1989
Long-time numerical solution of a parabolic equation with memory. Zbl 0801.65135
Thomée, Vidar; Wahlbin, Lars B.
1994
On the discretization in time of semilinear parabolic equations with nonsmooth initial data. Zbl 0632.65097
Crouzeix, Michel; Thomée, Vidar
1987
Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data. Zbl 0634.65110
Johnson, Claes; Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1987
From finite differences to finite elements. A short history of numerical analysis of partial differential equations. Zbl 0977.65001
Thomée, Vidar
2001
Discrete interior Schauder estimates for elliptic difference operators. Zbl 0176.15901
Thomee, V.
1968
Maximum-norm estimates for resolvents of elliptic finite element operators. Zbl 1028.65113
Bakaev, Nikolai Yu.; Thomée, Vidar; Wahlbin, Lars B.
2003
Stability of difference schemes in the maximum-norm. Zbl 0259.65086
Thomee, Vidar
1965
Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data. Zbl 0701.65091
Le Roux, Marie-Noëlle; Thomée, Vidar
1989
The lumped mass finite element method for a parabolic problem. Zbl 0576.65110
Chen, C. M.; Thomée, V.
1985
Error estimates for finite element methods for semilinear parabolic problems with nonsmooth data. Zbl 0617.65118
Thomée, V.
1986
Stability and analyticity in maximum-norm for simplical Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions. Zbl 0973.65079
Thomée, V.; Wahlbin, L. B.
2000
Parabolic finite element equations in nonconvex polygonal domains. Zbl 1108.65097
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.; Wahlbin, L. B.
2006
Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data. Zbl 0663.65110
Bramble, James H.; Pasciak, Joseph E.; Sammon, Peter H.; Thomée, Vidar
1989
Convergence estimates for essentially positive tpye discrete Dirichlet problems. Zbl 0217.21902
Bramble, J. H.; Hubbard, B. E.; Thomée, V.
1969
Partial differential equations with numerical methods. Paperback reprint. Zbl 1157.65001
2009
On the existence of maximum principles in parabolic finite element equations. Zbl 1128.65085
Thomée, Vidar; Wahlbin, Lars B.
2008
A numerical method for the Benjamin-Ono equation. Zbl 0916.65139
Thomée, V.; Vasudeva Murthy, A. S.
1998
Semidiscrete-least squares methods for a parabolic boundary value problem. Zbl 0268.65060
Bramble, James H.; Thomee, Vidar
1972
Error estimates for a finite element approximation of a minimal surface. Zbl 0302.65086
Johnsen, Claes; Thomee, Vidar
1975
On the rate of convergence for discrete initial-value problems. Zbl 0172.13902
Peetre, J.; Thomee, V.
1967
Finite difference methods for linear parabolic equations. Zbl 0875.65080
Thomée, Vidar
1990
A lumped mass finite-element method with quadrature for a nonlinear parabolic problem. Zbl 0591.65079
Nie, Yiyong; Thomée, Vidar
1985
Numerical methods for ultraparabolic equations. Zbl 0859.65108
Akrivis, G.; Crouzeix, M.; Thomée, V.
1994
Stability and convergence rates in $$L_ p$$ for certain difference schemes. Zbl 0208.16201
Brenner, P.; Thomée, V.
1970
Parabolic finite volume element equations in nonconvex polygonal domains. Zbl 1168.65051
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2009
Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation. Zbl 0663.65118
Larsson, Stig; Thomée, Vidar; Zhang, Naiying
1989
Mathematical theory of finite and boundary element methods. Lecture notes of the seminar ’Mathematische Theorie der finiten Element- und Randelementmethoden’ organized by the ’Deutsche Mathematiker-Vereinigung’ and held in Düsseldorf, Germany, from June 7th to 14th, 1987. Zbl 0701.00028
Schatz, Albert H.; Thomée, Vidar; Wendland, Wolfgang L.
1990
P9lygonal domain approximation in Dirichlet’s problem. Zbl 0246.35023
Thomee, Vidar
1973
Discrete time Galerkin methods for a parabolic boundary value problem. Zbl 0306.65073
Bramble, James H.; Thomee, Vidar
1974
Resolvent estimates for elliptic finite element operators in one dimension. Zbl 0806.65096
Crouzeix, M.; Larsson, S.; Thomée, V.
1994
Superconvergence of the Galerkin iterates for integral equations of the second kind. Zbl 0575.65131
Sloan, Ian H.; Thomée, Vidar
1985
Asymptotic behaviour of numerical solutions of an evolution equation with memory. Zbl 0882.65144
McLean, W.; Thomée, V.
1997
Maximum-norm-stability and error-estimates in Galerkin methods for parabolic equations in one space variable. Zbl 0515.65082
Thomee, Vidar; Wahlbin, Lars B.
1983
Estimates of the Friedrichs-Lewy type for mixed problems in the theory of linear hyperbolic differential equations in two independent variables. Zbl 0078.08601
Thomee, Vidar
1957
Some convergence estimates for semidiscrete type schemes for time- dependent nonselfadjoint parabolic equations. Zbl 0538.65078
Huang, Mingyou; Thomée, Vidar
1981
On nonnegativity preservation in finite element methods for subdiffusion equations. Zbl 1364.65197
Jin, Bangti; Lazarov, Raytcho; Thomée, Vidar; Zhou, Zhi
2017
Resolvent estimates in $$l_p$$ for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes. Zbl 0987.65093
Crouzeix, Michel; Thomée, Vidar
2001
Some error estimates for the lumped mass finite element method for a parabolic problem. Zbl 1251.65129
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2012
Pointwise bounds for discrete Green’s functions. Zbl 0212.17904
Bramble, J. H.; Thomée, V.
1969
A high order parallel method for time discretization of parabolic type equations based on Laplace transformation and quadrature. Zbl 1070.65108
Thomée, Vidar
2005
Elliptic difference operators and Dirichlet’s problem. Zbl 0143.38304
Thomée, Vidar
1964
On the backward Euler method for parabolic equations with rough initial data. Zbl 0482.65051
Huang, Mingyou; Thomee, Vidar
1982
Convergence rates of parabolic difference schemes for non-smooth data. Zbl 0282.65070
Thomee, Vidar; Wahlbin, Lars
1974
Some error estimates for the finite volume element method for a parabolic problem. Zbl 1285.65059
Chatzipantelidis, Panagiotis; Lazarov, Raytcho; Thomée, Vidar
2013
Parabolic difference operators. Zbl 0171.13804
Thomee, V.
1966
Existence proofs for mixed problems for hyperbolic differential equations in two independent variables by means of the continuity method. Zbl 0089.30204
Thomée, Vidar
1958
Unconditionally stable difference methods for mixed problems for quasi- linear hyperbolic systems in two dimensions. Zbl 0109.09603
Keller, Herbert B.; Thomee, V.
1962
On preservation of positivity in some finite element methods for the heat equation. Zbl 1327.65172
Chatzipantelidis, Panagiotis; Horváth, Zoltan; Thomée, Vidar
2015
Maximum-norm estimates for finite-element methods for a strongly damped wave equation. Zbl 1053.65077
Thomée, V.; Wahlbin, L. B.
2004
Estimates near discontinuities for some difference schemes. Zbl 0231.65074
Brenner, Philip; Thomee, Vidar
1971
A property of bounded normal operators in Hilbert space. Zbl 0194.15103
Björck, G.; Thomee, V.
1963
Long time behaviour of backward difference type methods for parabolic equations with memory in Banach space. Zbl 0913.65139
Bakaev, N. Yu.; Larsson, S.; Thomée, V.
1998
On the rate of convergence of some difference schemes for second order elliptic equations. Zbl 0172.20004
Bramble, J. H.; Kellogg, R. B.; Thomee, V.
1968
Difference methods for two-dimensional mixed problems for hyperbolic first order systems. Zbl 0104.32202
Thomee, Vidar
1961
A stable difference scheme for the mixed boundary problem for a hyperbolic, first-order system in two dimensions. Zbl 0107.11401
Thomee, V.
1962
An explicit-implicit splitting method for a convection-diffusion problem. Zbl 1420.65089
Thomée, Vidar; Vasudeva Murthy, A. S.
2019
On nonnegativity preservation in finite element methods for the heat equation with non-Dirichlet boundary conditions. Zbl 1407.65195
2018
On nonnegativity preservation in finite element methods for subdiffusion equations. Zbl 1364.65197
Jin, Bangti; Lazarov, Raytcho; Thomée, Vidar; Zhou, Zhi
2017
On preservation of positivity in some finite element methods for the heat equation. Zbl 1327.65172
Chatzipantelidis, Panagiotis; Horváth, Zoltan; Thomée, Vidar
2015
On positivity preservation in some finite element methods for the heat equation. Zbl 1360.65243
Thomée, V.
2015
Some error estimates for the finite volume element method for a parabolic problem. Zbl 1285.65059
Chatzipantelidis, Panagiotis; Lazarov, Raytcho; Thomée, Vidar
2013
Some error estimates for the lumped mass finite element method for a parabolic problem. Zbl 1251.65129
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2012
Iterative solution of shifted positive-definite linear systems arising in a numerical method for the heat equation based on Laplace transformation and quadrature. Zbl 1264.65046
Mclean, William; Thomée, Vidar
2011
Numerical solution via Laplace transforms of a fractional order evolution equation. Zbl 1195.65122
McLean, William; Thomée, Vidar
2010
Maximum-norm error analysis of a numerical solution via Laplace transformation and quadrature of a fractional-order evolution equation. Zbl 1416.65381
McLean, William; Thomée, Vidar
2010
On positivity and maximum-norm contractivity in time stepping methods for parabolic equations. Zbl 1283.65086
Schatz, A. H.; Thomée, V.; Wahlbin, L. B.
2010
Partial differential equations with numerical methods. Paperback reprint. Zbl 1157.65001
2009
Parabolic finite volume element equations in nonconvex polygonal domains. Zbl 1168.65051
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2009
On the existence of maximum principles in parabolic finite element equations. Zbl 1128.65085
Thomée, Vidar; Wahlbin, Lars B.
2008
Maximum-norm stability, smoothing and resolvent estimates for parabolic finite element equations. Zbl 1132.65086
Thomée, Vidar
2007
Galerkin finite element methods for parabolic problems. 2nd revised and expanded ed. Zbl 1105.65102
Thomée, Vidar
2006
Time discretization via Laplace transformation of an integro-differential equation of parabolic type. Zbl 1097.65131
McLean, William; Sloan, Ian H.; Thomée, Vidar
2006
Parabolic finite element equations in nonconvex polygonal domains. Zbl 1108.65097
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.; Wahlbin, L. B.
2006
Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations. Zbl 1116.65108
Bakaev, Nikolai Yu.; Crouzeix, Michel; Thomée, Vidar
2006
A high order parallel method for time discretization of parabolic type equations based on Laplace transformation and quadrature. Zbl 1070.65108
Thomée, Vidar
2005
Partial differential equations with numerical methods. Transl. from the English bei M. Krieger-Hauwede. (Partielle Differentialgleichungen und numerische Methoden.) Zbl 1065.65002
2005
Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. Zbl 1067.65092
Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V.
2004
Time discretization of an evolution equation via Laplace transforms. Zbl 1068.65146
McLean, William; Thomée, Vidar
2004
Maximum-norm estimates for finite-element methods for a strongly damped wave equation. Zbl 1053.65077
Thomée, V.; Wahlbin, L. B.
2004
A parallel method for time discretization of parabolic equations based on Laplace transformation and quadrature. Zbl 1022.65108
Sheen, Dongwoo; Sloan, Ian H.; Thomée, Vidar
2003
Partial differential equations with numerical methods. Zbl 1025.65002
2003
Maximum-norm estimates for resolvents of elliptic finite element operators. Zbl 1028.65113
Bakaev, Nikolai Yu.; Thomée, Vidar; Wahlbin, Lars B.
2003
From finite differences to finite elements. A short history of numerical analysis of partial differential equations. Zbl 0977.65001
Thomée, Vidar
2001
Resolvent estimates in $$l_p$$ for discrete Laplacians on irregular meshes and maximum-norm stability of parabolic finite difference schemes. Zbl 0987.65093
Crouzeix, Michel; Thomée, Vidar
2001
A parallel method for time-discretization of parabolic problems based on contour integral representation and quadrature. Zbl 0936.65109
Sheen, Dongwoo; Sloan, Ian H.; Thomée, Vidar
2000
Stability and analyticity in maximum-norm for simplical Lagrange finite element semidiscretizations of parabolic equations with Dirichlet boundary conditions. Zbl 0973.65079
Thomée, V.; Wahlbin, L. B.
2000
Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method. Zbl 0896.65090
Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1998
Stability, analyticity, and almost best approximation in maximum norm for parabolic finite element equations. Zbl 0932.65103
Schatz, A. H.; Thomée, V.; Wahlbin, L. B.
1998
A numerical method for the Benjamin-Ono equation. Zbl 0916.65139
Thomée, V.; Vasudeva Murthy, A. S.
1998
Long time behaviour of backward difference type methods for parabolic equations with memory in Banach space. Zbl 0913.65139
Bakaev, N. Yu.; Larsson, S.; Thomée, V.
1998
Backward Euler type methods for parabolic integro-differential equations in Banach space. Zbl 0905.65129
Bakaev, N. Yu.; Larsson, S.; Thomée, V.
1998
Galerkin finite element methods for parabolic problems. Zbl 0884.65097
Thomée, Vidar
1997
Asymptotic behaviour of numerical solutions of an evolution equation with memory. Zbl 0882.65144
McLean, W.; Thomée, V.
1997
Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term. Zbl 0852.65138
Lubich, Ch.; Sloan, I. H.; Thomée, V.
1996
Asymptotic behavior of semidiscrete finite element approximations of Biot’s consolidation problem. Zbl 0854.76053
Murad, Márcio A.; Thomée, Vidar; Loula, Abimael F. D.
1996
Discretization with variable time steps of an evolution equation with a positive-type memory term. Zbl 0858.65143
McLean, W.; Thomée, V.; Wahlbin, L. B.
1996
On multigrid methods for parabolic problems. Zbl 0831.65100
Larsson, S.; Thomée, V.; Zhou, S. Z.
1995
Approximate solution of $$u'=-A^ 2u$$ using a relation between $$\exp (-tA^ 2)$$ and $$\exp (itA)$$. Zbl 0840.65045
Thomée, V.; Vasudeva Murthy, A. S.
1995
Long-time numerical solution of a parabolic equation with memory. Zbl 0801.65135
Thomée, Vidar; Wahlbin, Lars B.
1994
Numerical methods for ultraparabolic equations. Zbl 0859.65108
Akrivis, G.; Crouzeix, M.; Thomée, V.
1994
Resolvent estimates for elliptic finite element operators in one dimension. Zbl 0806.65096
Crouzeix, M.; Larsson, S.; Thomée, V.
1994
Finite element methods for parabolic problems – Some steps in the evolution. Zbl 0818.65092
Thomée, Vidar
1994
Numerical solution of an evolution equation with a positive-type memory term. Zbl 0791.65105
McLean, W.; Thomée, V.
1993
The stability of rational approximations of analytic semigroups. Zbl 0783.65050
Crouzeix, M.; Larsson, S.; Piskarev, S.; Thomée, V.
1993
Completely discrete methods for parabolic equations with memory. Zbl 0878.65124
Thomée, V.
1993
Backward Euler type methods for parabolic integro-differential equations with nonsmooth data. Zbl 0834.65139
Thomée, Vidar; Zhang, Nai-Ying
1993
Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel. Zbl 0766.65120
Chen, C.; Thomée, V.; Wahlbin, L. B.
1992
Numerical methods for hyperbolic and parabolic integro-differential equations. Zbl 0764.65086
Pani, A. K.; Thomée, V.; Wahlbin, L. B.
1992
Approximate solution of O.D.E.s in Banach space rational approximation of semigroups. Zbl 0812.65044
Thomée, Vidar
1992
Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations. Zbl 0728.65117
Lin, Yanping; Thomée, Vidar; Wahlbin, Lars B.
1991
Finite-element methods for a strongly damped wave equation. Zbl 0718.65070
Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1991
An a posteriori error estimate and adaptive timestep control for a backward Euler discretization of a parabolic problem. Zbl 0701.65063
Johnson, Claes; Nie, Yi-Yong; Thomée, Vidar
1990
Finite difference methods for linear parabolic equations. Zbl 0875.65080
Thomée, Vidar
1990
Mathematical theory of finite and boundary element methods. Lecture notes of the seminar ’Mathematische Theorie der finiten Element- und Randelementmethoden’ organized by the ’Deutsche Mathematiker-Vereinigung’ and held in Düsseldorf, Germany, from June 7th to 14th, 1987. Zbl 0701.00028
Schatz, Albert H.; Thomée, Vidar; Wendland, Wolfgang L.
1990
Error estimates for semidiscrete finite element methods for parabolic integro-differential equations. Zbl 0673.65099
Thomée, Vidar; Zhang, Nai-Ying
1989
Superconvergence of the gradient in piecewise linear finite-element approximation to a parabolic problem. Zbl 0678.65079
Thomée, Vidar; Xu, Jin-Chao; Zhang, Nai-Ying
1989
Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data. Zbl 0701.65091
Le Roux, Marie-Noëlle; Thomée, Vidar
1989
Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data. Zbl 0663.65110
Bramble, James H.; Pasciak, Joseph E.; Sammon, Peter H.; Thomée, Vidar
1989
Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation. Zbl 0663.65118
Larsson, Stig; Thomée, Vidar; Zhang, Naiying
1989
Error estimates for spatially discrete approximations of semilinear parabolic equations with initial data of low regularity. Zbl 0674.65071
Crouzeix, M.; Thomée, V.; Wahlbin, L. B.
1989
On the numerical solution of integro-differential equations of parabolic type. Zbl 0658.65142
Thomée, Vidar
1988
The stability in $$L_ p$$ and $$W^ 1_ p$$ of the $$L_ 2$$-projection onto finite element function spaces. Zbl 0637.41034
Crouzeix, M.; Thomée, V.
1987
On the discretization in time of semilinear parabolic equations with nonsmooth initial data. Zbl 0632.65097
Crouzeix, Michel; Thomée, Vidar
1987
Error estimates for spatially discrete approximations of semilinear parabolic equations with nonsmooth initial data. Zbl 0634.65110
Johnson, Claes; Larsson, Stig; Thomée, Vidar; Wahlbin, Lars B.
1987
Time discretization of an integro-differential equation of parabolic type. Zbl 0608.65096
Sloan, I. H.; Thomée, V.
1986
Error estimates for finite element methods for semilinear parabolic problems with nonsmooth data. Zbl 0617.65118
Thomée, V.
1986
Time discretization of parabolic problems by the discontinuous Galerkin method. Zbl 0589.65070
Eriksson, Kenneth; Johnson, Claes; Thomée, Vidar
1985
The lumped mass finite element method for a parabolic problem. Zbl 0576.65110
Chen, C. M.; Thomée, V.
1985
A lumped mass finite-element method with quadrature for a nonlinear parabolic problem. Zbl 0591.65079
Nie, Yiyong; Thomée, Vidar
1985
Superconvergence of the Galerkin iterates for integral equations of the second kind. Zbl 0575.65131
Sloan, Ian H.; Thomée, Vidar
1985
Galerkin finite element methods for parabolic problems. Zbl 0528.65052
Thomee, Vidar
1984
Galerkin methods for singular boundary value problems in one space dimension. Zbl 0546.65055
Eriksson, Kenneth; Thomée, Vidar
1984
Maximum-norm-stability and error-estimates in Galerkin methods for parabolic equations in one space variable. Zbl 0515.65082
Thomee, Vidar; Wahlbin, Lars B.
1983
Single step methods for inhomogeneous linear differential equations in Banach space. Zbl 0477.65040
Brenner, Philip; Crouzeix, Michel; Thomee, Vidar
1982
On the backward Euler method for parabolic equations with rough initial data. Zbl 0482.65051
Huang, Mingyou; Thomee, Vidar
1982
Error estimates for some mixed finite element methods for parabolic type problems. Zbl 0476.65074
Johnson, Claes; Thomee, Vidar
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
Some convergence estimates for semidiscrete type schemes for time- dependent nonselfadjoint parabolic equations. Zbl 0538.65078
Huang, Mingyou; Thomée, Vidar
1981
Maximum norm stability and error estimates in parabolic finite element equations. Zbl 0414.65066
Schatz, A. H.; Thomee, V.; Wahlbin, L. B.
1980
Negative norm estimates and superconvergence in Galerkin methods for parabolic problems. Zbl 0454.65077
Thomee, Vidar
1980
On rational approximations of groups of operators. Zbl 0443.41013
Brenner, Philip; Thomee, Vidar
1980
Galerkin-finite element methods for parabolic equations. Zbl 0418.65050
Thomee, Vidar
1980
On rational approximations of semigroups. Zbl 0413.41011
Brenner, Philip; Thomee, Vidar
1979
Some interior estimates for semidiscrete Galerkin approximations for parabolic equations. Zbl 0419.65073
Thomee, Vidar
1979
Some convergence estimates for semidiscrete Galerkin type approximations for parabolic equations. Zbl 0364.65084
Bramble, J. H.; Schatz, A. H.; Thomee, V.; Wahlbin, L. B.
1977
High order local approximations to derivatives in the finite element method. Zbl 0367.65055
Thomee, Vidar
1977
Single step Galerkin approximations for parabolic problems. Zbl 0378.65061
Baker, Garth A.; Bramble, James H.; Thomee, Vidar
1977
Convergence analysis of finite difference schemes for semi-linear initial-value problems. Zbl 0332.35006
Löfström, J.; Thomee, V.
1976
Besov spaces and applications to difference methods for initial value problems. Zbl 0294.35002
Brenner, Philip; Thomee, Vidar; Wahlbin, Lars B.
1975
On Galerkin methods in semilinear parabolic problems. Zbl 0307.35007
Thomee, Vidar; Wahlbin, Lars
1975
Error estimates for a finite element approximation of a minimal surface. Zbl 0302.65086
Johnsen, Claes; Thomee, Vidar
1975
Convergence estimates for Galerkin methods for variable coefficient initial value problems. Zbl 0292.65052
Thomee, Vidar; Wendroff, Burton
1974
Discrete time Galerkin methods for a parabolic boundary value problem. Zbl 0306.65073
Bramble, James H.; Thomee, Vidar
1974
Convergence rates of parabolic difference schemes for non-smooth data. Zbl 0282.65070
Thomee, Vidar; Wahlbin, Lars
1974
Interior maximum norm estimates for some simple finite element methods. Zbl 0301.65065
Bramble, J. H.; Thomee, V.
1974
...and 34 more Documents
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#### Cited by 2,620 Authors

 50 Xu, Da 43 Thomée, Vidar 32 Pani, Amiya Kumar 28 Li, Hong 27 Li, Buyang 25 Larsson, Stig 24 Sinha, Rajen Kumar 23 Zhou, Zhi 22 Vabishchevich, Pëtr Nikolaevich 20 Liu, Yang 18 Shi, Dongyang 18 Zhang, Zhimin 17 Akrivis, Georgios D. 17 Burman, Erik 17 Hansbo, Peter 17 Wang, Hong 16 Chen, Yanping 16 Dougalis, Vassilios A. 16 Luo, Zhendong 16 Vexler, Boris 15 Jin, Bangti 15 Kovács, Mihály 15 Lazarov, Raytcho D. 15 McLean, William 15 Nochetto, Ricardo Horacio 14 Bramble, James H. 14 Leykekhman, Dmitriy 14 Wahlbin, Lars B. 14 Zheng, Xiangcheng 13 Lubich, Christian 13 Makridakis, Charalambos G. 13 Mustapha, Kassem 13 Omrani, Khaled 13 Palencia, Cesar 12 Chen, Chuanjun 12 Ferreira, José Augusto 12 Sun, Weiwei 12 Wang, Jilu 12 Yan, Yubin 11 Karaa, Samir 11 Larson, Mats G. 11 Lin, Yanping 11 Rui, Hongxing 11 Spijker, Marc N. 10 Cockburn, Bernardo 10 Crouzeix, Michel 10 Ryan, Jennifer K. 10 Yang, Min 9 Chen, Chuanmiao 9 Chen, Zhangxin 9 Deka, Bhupen 9 Deng, Weihua 9 Gao, Huadong 9 Gaspar, Francisco José 9 He, Siriguleng 9 Hu, Xiaozhe 9 Huang, Yunqing 9 Layton, William J. 9 Ma, Jingtang 9 Schwab, Christoph 8 Babuška, Ivo 8 Bakaev, Nikolai Yu. 8 Cao, Waixiang 8 Chrysafinos, Konstantinos 8 Emmrich, Etienne 8 Feng, Xinlong 8 Gavrilyuk, Ivan P. 8 Hackbusch, Wolfgang 8 Karakashian, Ohannes A. 8 Khaliq, Abdul Q. M. 8 Křížek, Michal 8 Li, Binjie 8 Lin, Qun 8 Makarov, Volodymyr Leonidovych 8 Marcozzi, Michael D. 8 Matthies, Gunar 8 Ostermann, Alexander 8 Piskarëv, S. I. 8 Rannacher, Rolf 8 Rodrigo, Carmen 8 Sayas, Francisco-Javier 8 Stynes, Martin 8 Xie, Xiaoping 7 Ashyralyev, Allaberen 7 Bi, Chunjia 7 Bradji, Abdallah 7 Ewing, Richard Edward 7 Faragó, István 7 Fernández, Miguel Ángel 7 Gunzburger, Max D. 7 Huang, Jianguo 7 Lasiecka, Irena 7 Li, Jian 7 Murad, Márcio Arab 7 Nie, Daxin 7 Prohl, Andreas 7 Saito, Norikazu 7 Schatz, Alfred H. 7 Sun, Jing 7 Tambue, Antoine ...and 2,520 more Authors
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#### Cited in 267 Serials

 199 Mathematics of Computation 140 Journal of Computational and Applied Mathematics 133 Numerische Mathematik 130 Journal of Scientific Computing 121 Computers & Mathematics with Applications 119 Applied Numerical Mathematics 103 Computer Methods in Applied Mechanics and Engineering 97 Applied Mathematics and Computation 70 Numerical Methods for Partial Differential Equations 54 SIAM Journal on Numerical Analysis 47 Journal of Mathematical Analysis and Applications 45 Journal of Computational Physics 45 BIT 39 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 35 SIAM Journal on Scientific Computing 33 Numerical Functional Analysis and Optimization 26 Calcolo 26 Numerical Algorithms 24 RAIRO. Modélisation Mathématique et Analyse Numérique 21 Advances in Computational Mathematics 20 Applied Mathematics Letters 19 Applicable Analysis 19 Journal of Applied Mathematics and Computing 18 Mathematics and Computers in Simulation 18 Applications of Mathematics 17 Computational Methods in Applied Mathematics 14 International Journal of Computer Mathematics 14 Computational and Applied Mathematics 14 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 13 Mathematical Methods in the Applied Sciences 13 Computing 13 Journal of Integral Equations and Applications 13 Advances in Applied Mathematics and Mechanics 12 International Journal for Numerical Methods in Engineering 12 RAIRO. Analyse Numérique 12 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 11 Applied Mathematical Modelling 11 Advances in Difference Equations 10 Mathematical Problems in Engineering 9 Fractional Calculus & Applied Analysis 9 Discrete and Continuous Dynamical Systems. Series B 9 Communications in Computational Physics 8 Journal of Differential Equations 8 Journal of Functional Analysis 8 Computational Geosciences 8 Differential Equations 8 Journal of Numerical Mathematics 8 Science China. Mathematics 7 Archive for Rational Mechanics and Analysis 7 Computers and Fluids 7 Journal of Approximation Theory 7 Applied Mathematics and Mechanics. (English Edition) 7 Computational Mathematics and Mathematical Physics 6 Applied Mathematics and Optimization 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Proceedings of the American Mathematical Society 6 Japan Journal of Industrial and Applied Mathematics 6 Journal of Mathematical Sciences (New York) 6 Engineering Analysis with Boundary Elements 6 Communications in Nonlinear Science and Numerical Simulation 6 The ANZIAM Journal 6 Journal of Applied Mathematics 5 Annali di Matematica Pura ed Applicata. Serie Quarta 5 Aplikace Matematiky 5 SIAM Journal on Control and Optimization 5 Acta Mathematicae Applicatae Sinica. English Series 5 Linear Algebra and its Applications 5 Applied Mathematics. Series B (English Edition) 5 Journal of Inverse and Ill-Posed Problems 5 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 5 Abstract and Applied Analysis 5 Journal of Inequalities and Applications 5 Journal of Evolution Equations 5 BIT. Nordisk Tidskrift for Informationsbehandling 5 Frontiers of Mathematics in China 4 Lithuanian Mathematical Journal 4 Ukrainian Mathematical Journal 4 Mathematische Zeitschrift 4 Transactions of the American Mathematical Society 4 Mathematical and Computer Modelling 4 Science in China. Series A 4 Journal of Difference Equations and Applications 4 Discrete Dynamics in Nature and Society 4 Multiscale Modeling & Simulation 4 Boundary Value Problems 4 Mathematical Control and Related Fields 4 Nonlinear Analysis. Theory, Methods & Applications 4 Electronic Research Archive 3 Bulletin of the Australian Mathematical Society 3 Computer Physics Communications 3 Communications on Pure and Applied Mathematics 3 International Journal for Numerical Methods in Fluids 3 Inverse Problems 3 Israel Journal of Mathematics 3 Journal of the Franklin Institute 3 ZAMP. Zeitschrift für angewandte Mathematik und Physik 3 Acta Applicandae Mathematicae 3 Computational Mechanics 3 Journal de Mathématiques Pures et Appliquées. Neuvième Série 3 Computers and Mathematics with Applications. Part A ...and 167 more Serials
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#### Cited in 45 Fields

 2,017 Numerical analysis (65-XX) 1,291 Partial differential equations (35-XX) 339 Fluid mechanics (76-XX) 195 Integral equations (45-XX) 175 Mechanics of deformable solids (74-XX) 118 Ordinary differential equations (34-XX) 88 Operator theory (47-XX) 88 Probability theory and stochastic processes (60-XX) 86 Calculus of variations and optimal control; optimization (49-XX) 73 Real functions (26-XX) 65 Biology and other natural sciences (92-XX) 57 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 43 Classical thermodynamics, heat transfer (80-XX) 41 Optics, electromagnetic theory (78-XX) 36 Approximations and expansions (41-XX) 35 Systems theory; control (93-XX) 33 Integral transforms, operational calculus (44-XX) 33 Functional analysis (46-XX) 26 Statistical mechanics, structure of matter (82-XX) 25 Geophysics (86-XX) 19 Harmonic analysis on Euclidean spaces (42-XX) 16 Quantum theory (81-XX) 15 Difference and functional equations (39-XX) 14 Dynamical systems and ergodic theory (37-XX) 13 Linear and multilinear algebra; matrix theory (15-XX) 12 Computer science (68-XX) 11 Special functions (33-XX) 7 Functions of a complex variable (30-XX) 7 Potential theory (31-XX) 7 Operations research, mathematical programming (90-XX) 6 Mechanics of particles and systems (70-XX) 5 Differential geometry (53-XX) 5 Global analysis, analysis on manifolds (58-XX) 4 Statistics (62-XX) 4 Information and communication theory, circuits (94-XX) 3 History and biography (01-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Category theory; homological algebra (18-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Sequences, series, summability (40-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX)

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