Optimal Order FEM for a Coupled Eigenvalue Problem on 2D Overlapping Domains

Authors:
A. B. Andreev;M. R. Racheva
Affiliations:
Department of Informatics, Technical University of Gabrovo, Gabrovo, Bulgaria 5300;Department of Mathematics, Technical University of Gabrovo, Gabrovo, Bulgaria 5300
Venue:
Numerical Analysis and Its Applications
Year:
2009

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Abstract

In this paper we present a numerical approach to a nonstandard second-order elliptic eigenvalue problem defined on two overlapping rectangular domains with a nonlocal (integral) boundary condition. Usually, for this class of problems error estimates are suboptimal. By introducing suitable degrees of freedom and a corresponding interpolation operator we derive optimal order finite element approximation. Numerical results illustrate the efficiency of the proposed method.