A note on the effect of numerical quadrature in finite element eigenvalue approximation. (English) Zbl 0748.65078

Banerjee, Uday

Numer. Math. 61, No. 2, 145-152 (1992).

This (concise!) paper gives a deeper insight into the results of the author’s and J. E. Osborn’s earlier paper (with almost the same title) [Numer. Math. 56, No. 8, 735-762 (1990; Zbl 0693.65071)]. It was shown there that the finite element approximation of the eigenpairs of elliptic differential operators (with dimensions 1, 2, or 3), when the elements of the underlying matrices are approximated by numerical quadrature, yields optimal order of convergence when the precision of the integration is one higher than that used for the finite element approximation of the solution of the corresponding source problem.
Here are the refined results: the original assumption is indeed sharp, to obtain the optimal order of convergence for the approximate eigenvalues. But one does not require to increase the precision of the quadrature to obtain the optimal order of convergence for the eigenvectors.

Reviewer: E.Lanckau (Chemnitz)

MSC:

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
35P15	Estimates of eigenvalues in context of PDEs

Keywords:

effect of numerical quadrature; finite element methods; eigenpairs; elliptic differential operators; optimal order of convergence; eigenvalues; eigenvectors

Citations:

Zbl 0693.65071

References:

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