An abstract spectral approximation theorem from the theory of semigroups

We show that spectral approximations converge for a broad class of partial differential equations. In particular, if the governing differential operator generates a strongly continuous linear contraction semigroup in a Hilbert space and the approximating subspaces satisfy a certain invariance condit...

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Bibliographic Details
Published in:Applied mathematics and computation 1992-02, Vol.47 (2), p.185-199
Main Author: Oppenheimer, Seth F.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Operator theory
Sciences and techniques of general use
Online Access:Get full text
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Summary:We show that spectral approximations converge for a broad class of partial differential equations. In particular, if the governing differential operator generates a strongly continuous linear contraction semigroup in a Hilbert space and the approximating subspaces satisfy a certain invariance condition with respect to the differential operator, then the standard spectral approximation scheme, as well as a slight modification thereof, converges in the Hilbert space norm.
ISSN:0096-3003
1873-5649
DOI:10.1016/0096-3003(92)90046-4