On the stability of the spectral Galerkin approximation

We study stability properties of the spectral Galerkin approximation of the solutions of semilinear problems. Assuming that the data of the problem are known within a certain error, we investigate when the solution of the Galerkin approximate equation provides a desired accuracy uniformly with respe...

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Bibliographic Details
Published inNumerical algorithms Vol. 14; no. 1-3; pp. 165 - 178
Main Author Lyashenko, Andrei A
Format Journal Article
LanguageEnglish
Published New York Springer Nature B.V 01.01.1997
Subjects
Approximation
Error analysis
Exact solutions
Galerkin method
Mathematical analysis
Perturbation
Stability
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Summary:We study stability properties of the spectral Galerkin approximation of the solutions of semilinear problems. Assuming that the data of the problem are known within a certain error, we investigate when the solution of the Galerkin approximate equation provides a desired accuracy uniformly with respect to small perturbations of the data. We show that for certain classes of semilinear problems an additional compactness assumption is sufficient to assure that the spectral Galerkin method provides an accurate approximation to the exact solution uniformly with respect to small perturbations of the data.
ISSN:1017-1398
1572-9265
DOI:10.1023/A:1019160913159