Approximation du spectre d'un operateur lineaire; application aux operateurs differentiels elliptiques non autoadjoints

Abstract

To be computed, the eigenvalues of a closed linear operatorT in a Banach space are usually approximated by the eigenvalues ofT h, a linear operator approximatingT in a finite dimensional space (for example, finite difference method, Galerkin method),h is a parameter which tends to 0. This approximation is studied in [2]; stability ofT h implies the continuity of the spectrum ofT h, whenh tends to 0. We present here a new kind of sufficient condition. For that purpose, we disconnect the continuity of the spectrum ofT h into lower and upper semicontinuities. And we give two different criteria for these semi-continuities. Applications to the approximation of nonselfadjoint elliptic operators by finite difference schemes, are given.