Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^sup d^ , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the [theta]-method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized o...

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Bibliographic Details
Published inApplications of mathematics (Prague) Vol. 48; no. 2; pp. 111 - 128
Main Authors Faragó, István, Korotov, Sergey, Neittaanmäki, Pekka
Format Journal Article
LanguageEnglish
Published Prague Springer Nature B.V 01.04.2003
Subjects
Applications of mathematics
Approximation
Boundary conditions
Convergence
Discretization
Finite element analysis
Galerkin methods
Mathematical analysis
Projection
Studies
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Summary:We solve a linear parabolic equation in ^sup d^ , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the [theta]-method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.[PUBLICATION ABSTRACT]
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0862-7940
1572-9109
DOI:10.1023/A:1026042110602