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Spectral approximation of variationally formulated eigenvalue problems on curved domains. (English) Zbl 1171.65075
Summary: This paper is concerned with the spectral approximation of variationally formulated eigenvalue problems posed on curved domains. As an example of the present theory, convergence and optimal error estimates are proved for the piecewise linear finite element approximation of the eigenvalues and eigenfunctions of a second order elliptic differential operator on a general curved three-dimensional domain.

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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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