New Approach of FEM for Eigenvalue Problems with Non-local Transition Conditions

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

Citing 3
Cited 0

A finite element method for elliptic eigenvalue problems in a multi-component domain in 2D with non-local Dirichlet transition conditions

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

Numerical Analysis and Its Applications

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Abstract

This paper is considered with the finite element method (FEM) for second order eigenvalue problems on a bounded multi-compo- nent domain in the plane. Non-local transition conditions on the interfaces between any two adjacent subdomains are imposed. A new finite element approach is proposed based on much more comprehensible theoretical proofs obtained under lower regularity requirements. The utility of this strategy when superconvergent postprocessing procedure is used as well as the numerical implementation are discussed. Finally, some numerical results are given.