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On a variational approximation method for a class of elliptic eigenvalue problems in composite structures


Authors: M. Vanmaele and R. Van Keer
Journal: Math. Comp. 65 (1996), 999-1017
MSC (1991): Primary 65N25, 65N30, 65D30
DOI: https://doi.org/10.1090/S0025-5718-96-00741-7
MathSciNet review: 1344623
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Abstract: We consider a second-order elliptic eigenvalue problem on a convex polygonal domain, divided in $M$ nonoverlapping subdomains. The conormal derivative of the unknown function is continuous on the interfaces, while the function itself is discontinuous. We present a general finite element method to obtain a numerical solution of the eigenvalue problem, starting from a nonstandard formally equivalent variational formulation in an abstract setting in product Hilbert spaces. We use standard Lagrange finite element spaces on the subdomains. Moreover, the bilinear forms are approximated by suitable numerical quadrature formulas. We obtain error estimates for both the eigenfunctions and the eigenvalues, allowing for the case of multiple exact eigenvalues, by a pure variational method.


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Additional Information

M. Vanmaele
Affiliation: Department of Mathematical Analysis, Engineering Faculty, University of Gent, Galglaan 2, 9000 Gent, Belgium
Email: mv@cage.rug.ac.be

R. Van Keer
Affiliation: Department of Mathematical Analysis, Engineering Faculty, University of Gent, Galglaan 2, 9000 Gent, Belgium
Email: rvk@cage.rug.ac.be

DOI: https://doi.org/10.1090/S0025-5718-96-00741-7
Received by editor(s): August 23, 1993
Received by editor(s) in revised form: January 23, 1995
Article copyright: © Copyright 1996 American Mathematical Society

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