An abstract spectral approximation theorem from the theory of semigroups

摘要

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.