An abstract spectral approximation theorem from the theory of semigroups

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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.

Original languageEnglish (US)
Pages (from-to)185-199
Number of pages15
JournalApplied Mathematics and Computation
Issue number2-3
StatePublished - Feb 1992
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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