Abstract
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 language | English (US) |
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Pages (from-to) | 185-199 |
Number of pages | 15 |
Journal | Applied Mathematics and Computation |
Volume | 47 |
Issue number | 2-3 |
DOIs | |
State | Published - Feb 1992 |
Externally published | Yes |
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics