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Error estimates for a finite element method with numerical quadrature for a class of elliptic eigenvalue problems. (English) Zbl 0760.65096
Numerical methods, Proc. Conf., Miskolc/Hungary 1990, Colloq. Math. Soc. János Bolyai 59, 267-282 (1991).
[For the entire collection see Zbl 0741.00058.]
Error estimates for both the eigenvalues and the eigenfunctions of elliptic eigenvalue problems are derived, including the case of multiple exact eigenvalues. The error estimates are derived including the discretization error (a linear triangular or bilinear rectangular finite element method) as well as the error arising from the application of quadrature formulae. It is found out that the numerical quadrature formula used does not affect the order of convergence of the finite element method.

65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35P15 Estimates of eigenvalues in context of PDEs