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Finite element analysis of a coupling eigenvalue problem on overlapping domains. (English) Zbl 0988.65100
A nonstandard elliptic eigenvalue problem on a rectangular domain, consisting of two overlapping rectangles, where the interaction is expressed through an integral coupling condition is considered. Finite element (FE) discretizations with and without numerical quadrature are derived The error analysis is affected by the nonlocal coupling condition, which requires the introduction and error estimation of a suitably modified Lagrange interpolant on the FE mesh. As a consequence, the resulting error estimates are suboptimal compared to the ones for the classical eigenvalue problems.

MSC:
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N15 Error bounds 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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