Optimal convergence rates for semidiscrete approximations of parabolic problems with nonsmooth boundary data

We consider semidiscrete approximations of parabolic boundary value problems based on an elliptic approximation by J. Nitsche, in which the approximating subspaces are not subject to any boundary conditions. Optimal L p (L 2 ) error estimates are derived for both smooth and nonsmooth boundary data....

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Bibliographic Details
Published inNumerical functional analysis and optimization Vol. 12; no. 5-6; pp. 469 - 485
Main Authors Choudury, Gilbert, Lasiecka, Irena
Format Journal Article
LanguageEnglish
Published Philadelphia, PA Marcel Dekker, Inc 01.01.1991
Taylor & Francis
Subjects
Exact sciences and technology
Mathematics
Nitsche's method
Numerical analysis
Numerical analysis. Scientific computation
Parabolic Boundary-Value Problems
Partial differential equations, boundary value problems
Sciences and techniques of general use
Semidiscrete Approximation
Convergence rate
Parabolic equation
Semigroup
Boundary value problem
Error estimation
Singular integral
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ISSN0163-0563
1532-2467
DOI10.1080/01630569108816443

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Summary:We consider semidiscrete approximations of parabolic boundary value problems based on an elliptic approximation by J. Nitsche, in which the approximating subspaces are not subject to any boundary conditions. Optimal L p (L 2 ) error estimates are derived for both smooth and nonsmooth boundary data. The approach is based on semigroup theory combined with the theory of singular integrals.
ISSN:0163-0563
1532-2467
DOI:10.1080/01630569108816443