Estimate for the Errors in Eigenvalue and Eigenvector Approximation by Galerkin Methods, with Particular Attention to the Case of Multiple Eigenvalues

摘要

Refined estimates for the errors in eigenvalue and eigenvector approximation by finite element, or, more generally, Galerkin methods, as they apply to self-adjoint problems, are presented. Particular attention is given to the case of multiple eigenvalues. The results are new in this case. The proof is based on a novel approach which yields the known results for simple eigenvalues in a simple way. Numerical computations are presented and analyzed in light of the theoretical results.