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External finite-element approximations of eigenfunctions in the case of multiple eigenvalues. (English) Zbl 0811.65090
The paper deals with the finite element analysis of second-order elliptic eigenvalue problems when the domains \(\Omega_ h\) are not contained in the original domain \(\Omega\subset \mathbb{R}^ 2\). The main aim of the paper is to study the convergence of approximate eigenfunctionals in the case of multiple exact eigenvalues, extending an approach formerly established by the authors in the case of simple eigenvalues. It differs from the approach of I. Babuška and J. E. Osborn [Math. Comput. 52, No. 186, 275-297 (1989; Zbl 0675.65108)] in that no use is made of operator theory.

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
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