Optimal Order Finite Element Method for a Coupled Eigenvalue Problem on 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:
Large-Scale Scientific Computing
Year:
2009

Citing 3
Cited 0

Finite element analysis of a coupling eigenvalue problem on overlapping domains

Journal of Computational and Applied Mathematics
Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
One-Dimensional patch-recovery finite element method for fourth-order elliptic problems

NAA'04 Proceedings of the Third international conference on Numerical Analysis and its Applications

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Abstract

The aim of this paper is to present a new finite element approach applied to a nonstandard second order elliptic eigenvalue problem, defined on two overlapping domains. We derive optimal error estimates as distinguished from [1], where they are suboptimal. For this purpose we introduce a suitable modified degrees of freedom and a corresponding interpolation operator. In order to fix the ideas and to avoid technical difficulties, we consider an one-dimensional case. The conclusive part presents numerical results.