Thomée, Vidar 1933
Overview
Works:  85 works in 307 publications in 5 languages and 3,139 library holdings 

Roles:  Author, Editor, Other 
Classifications:  QA374, 515.353 
Publication Timeline
.
Most widely held works by
Vidar Thomée
Galerkin finite element methods for parabolic problems by
Vidar Thomée(
Book
)
58 editions published between 1984 and 2010 in 4 languages and held by 862 WorldCat member libraries worldwide
Surveying the mathematics of Galerkin finite element method as applied to parabolic equations, this textbook's approach is based on discretizing in the spatial variables by Galerkin's method. Piecewise polynomial trial functions are used, and time stepping methods are applied
58 editions published between 1984 and 2010 in 4 languages and held by 862 WorldCat member libraries worldwide
Surveying the mathematics of Galerkin finite element method as applied to parabolic equations, this textbook's approach is based on discretizing in the spatial variables by Galerkin's method. Piecewise polynomial trial functions are used, and time stepping methods are applied
Partial differential equations with numerical methods by
S Larsson(
Book
)
35 editions published between 2003 and 2009 in English and German and held by 435 WorldCat member libraries worldwide
Covers the integration of the theory of linear Partial Differential Equations and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, this text contains chapters on the mathematical theory of the differential equation, finite difference methods, and finite element methods
35 editions published between 2003 and 2009 in English and German and held by 435 WorldCat member libraries worldwide
Covers the integration of the theory of linear Partial Differential Equations and the numerical solution of such equations. For each type of PDE, elliptic, parabolic, and hyperbolic, this text contains chapters on the mathematical theory of the differential equation, finite difference methods, and finite element methods
Besov spaces and applications to difference methods for initial value problems by
Philip Brenner(
Book
)
21 editions published between 1975 and 2008 in 3 languages and held by 429 WorldCat member libraries worldwide
21 editions published between 1975 and 2008 in 3 languages and held by 429 WorldCat member libraries worldwide
Mathematical theory of finite and boundary element methods by
Alfred H Schatz(
Book
)
15 editions published in 1990 in English and German and held by 242 WorldCat member libraries worldwide
These are the lecture notes of the seminar "Mathematische Theorie der finiten Element und Randelementmethoden" organized by the "Deutsche MathematikerVereinigung" and held in Düsseldorf from June 7th  14th 1987. Finite element methods nowadays belong to the standard routines for the computation of solutions to boundary and initial boundary value problems of partial differential equations with many applications as e.g. in elasticity and thermoelasticity, fluid mechanics, acoustics, electromagnetics, scattering and diffusion. These methods also stimulated the development of corresponding mathematical numerical analysis. The seminar as well as these notes consist of three parts: I. An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems by A.H. Schatz II. On Finite Elements for Parabolic Problems by V. Thomée III. Boundary Element Methods for Elliptic Problems by W.L. Wendland. As a valuable addition to the standard literature in this field, these notes provide an introduction and overview of the three different topics which shed light on recent research
15 editions published in 1990 in English and German and held by 242 WorldCat member libraries worldwide
These are the lecture notes of the seminar "Mathematische Theorie der finiten Element und Randelementmethoden" organized by the "Deutsche MathematikerVereinigung" and held in Düsseldorf from June 7th  14th 1987. Finite element methods nowadays belong to the standard routines for the computation of solutions to boundary and initial boundary value problems of partial differential equations with many applications as e.g. in elasticity and thermoelasticity, fluid mechanics, acoustics, electromagnetics, scattering and diffusion. These methods also stimulated the development of corresponding mathematical numerical analysis. The seminar as well as these notes consist of three parts: I. An Analysis of the Finite Element Method for Second Order Elliptic Boundary Value Problems by A.H. Schatz II. On Finite Elements for Parabolic Problems by V. Thomée III. Boundary Element Methods for Elliptic Problems by W.L. Wendland. As a valuable addition to the standard literature in this field, these notes provide an introduction and overview of the three different topics which shed light on recent research
Partielle Differentialgleichungen und numerische Methoden by
S Larsson(
)
2 editions published in 2005 in German and held by 28 WorldCat member libraries worldwide
2 editions published in 2005 in German and held by 28 WorldCat member libraries worldwide
Some results concerning boundary problems for partial differential equations by
Vidar Thomée(
Book
)
4 editions published in 1959 in English and Swedish and held by 5 WorldCat member libraries worldwide
4 editions published in 1959 in English and Swedish and held by 5 WorldCat member libraries worldwide
Polygonal Domain Approximation in Dirichlet's Problem by
Vidar Thomée(
Book
)
5 editions published in 1971 in English and held by 5 WorldCat member libraries worldwide
Consider Dirichlet's problem with vanishing boundary values for Poisson's equation in a smooth domain omega in the plane. In the paper upper and lower bounds with respect to different norms are given for the error and the gradient of the error introduced by approximating omega by a polygonal domain omega sub h with sidelengths at most h. (Author)
5 editions published in 1971 in English and held by 5 WorldCat member libraries worldwide
Consider Dirichlet's problem with vanishing boundary values for Poisson's equation in a smooth domain omega in the plane. In the paper upper and lower bounds with respect to different norms are given for the error and the gradient of the error introduced by approximating omega by a polygonal domain omega sub h with sidelengths at most h. (Author)
Negative norm estimates and superconvergence in Galerkin methods for parabolic problems by
Vidar Thomée(
Book
)
4 editions published in 1978 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1978 in English and held by 4 WorldCat member libraries worldwide
Numerical solution of parabolic integrodifferential equations by the discontinuous Galerkin method by S Larsson(
Book
)
3 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 4 WorldCat member libraries worldwide
On rational approximations of groups of operators by
Philip Brenner(
Book
)
4 editions published in 1978 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1978 in English and held by 4 WorldCat member libraries worldwide
Spline Approximation and Difference Schemes for the Heat Equation by
Vidar Thomée(
Book
)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
It is proved that the spline approximation by Galerkin's method of the solution of the initialvalue problem for the heat equation can be considered as the successive application of an associated finite difference operator and a spline interpolation operator. If the splines considered are of order mu, the finite difference operator is parabolic and accurate of order 2mu  2. Some consequences of this fact are discussed. (Author)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
It is proved that the spline approximation by Galerkin's method of the solution of the initialvalue problem for the heat equation can be considered as the successive application of an associated finite difference operator and a spline interpolation operator. If the splines considered are of order mu, the finite difference operator is parabolic and accurate of order 2mu  2. Some consequences of this fact are discussed. (Author)
An a posteriori error estimate and automatic time step control for a backward Euler discretization of a parabolic problem by
Claes Johnson(
Book
)
4 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1985 in English and held by 4 WorldCat member libraries worldwide
Stability, analyticity, and almost best approximation in maximumnorm for parabolic finite element equations by
Alfred H Schatz(
Book
)
3 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Nonsmooth data error estimates for approximations of an evolution equation with a positive type memory term by
Christian Lubich(
Book
)
4 editions published between 1994 and 1995 in English and held by 4 WorldCat member libraries worldwide
4 editions published between 1994 and 1995 in English and held by 4 WorldCat member libraries worldwide
Projection methods for dirichlet's problem in approximating polygonal domains with boundary value corrections by
J. H Bramble(
Book
)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Accurate approximate methods for solving Dirichlet's problem in a plane domain which consist in applying projection methods on an approximating polygonal domain are described and analyzed. (Author)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Accurate approximate methods for solving Dirichlet's problem in a plane domain which consist in applying projection methods on an approximating polygonal domain are described and analyzed. (Author)
Galerkin methods for singular boundary value problems in one space dimension by
K Eriksson(
Book
)
4 editions published in 1982 in English and held by 4 WorldCat member libraries worldwide
4 editions published in 1982 in English and held by 4 WorldCat member libraries worldwide
A numerical method for the BenjaminOno equation by
Vidar Thomée(
Book
)
3 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
3 editions published in 1997 in English and held by 4 WorldCat member libraries worldwide
Discrete Time Galerkin Methods for a Parabolic Boundary Value Problem by
J. H Bramble(
Book
)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Single step discrete time Galerkin methods for the mixed initialboundary value problem for the heat equation are studied. Two general theoreis leading to error estimates are developed. Among the examples analyzed in the application of these theories are methods in which the related quadratic form is required to be definite only the subspace of approximating functions and two classes containing methods of arbitrary given order of accuracy, one requiring satisfaction of certain boundary conditions by the elements of the subspace, the other making no such requirements. (Author)
4 editions published in 1972 in English and held by 4 WorldCat member libraries worldwide
Single step discrete time Galerkin methods for the mixed initialboundary value problem for the heat equation are studied. Two general theoreis leading to error estimates are developed. Among the examples analyzed in the application of these theories are methods in which the related quadratic form is required to be definite only the subspace of approximating functions and two classes containing methods of arbitrary given order of accuracy, one requiring satisfaction of certain boundary conditions by the elements of the subspace, the other making no such requirements. (Author)
Error estimates for spatially discrete approximations of semilinear parabolic equations with initial data of low regularity by
Michel Crouzeix(
Book
)
5 editions published between 1987 and 1988 in English and held by 3 WorldCat member libraries worldwide
5 editions published between 1987 and 1988 in English and held by 3 WorldCat member libraries worldwide
Besov Spaces and Applications to Difference Methods for Initial Value Problems by
R. P Brenner(
)
1 edition published in 1975 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 0 WorldCat member libraries worldwide
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Approximation theory Banach spaces Besov spaces Boundary element methods Boundary value problems Boundary value problemsNumerical solutions Differential equations, Linear Differential equations, Parabolic Differential equations, ParabolicNumerical solutions Differential equations, Partial Differential equations, PartialNumerical solutions Dirichlet problem Engineering mathematics Error functions Finite differences Finite element method Galerkin methods Global analysis (Mathematics) Heat equation Initial value problems Integrodifferential equations Mathematical physics Mathematics Nonsmooth optimization Numerical analysis Operator theory Physics Poisson's equation Spline theory