Approximation theory methods for solving elliptic eigenvalue problems
Identifieur interne : 001230 ( Istex/Curation ); précédent : 001229; suivant : 001231Approximation theory methods for solving elliptic eigenvalue problems
Auteurs : G. Still [Pays-Bas]Source :
- ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik [ 0044-2267 ] ; 2003-07-07.
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Abstract
Eigenvalue problems with elliptic operators L on a domain G ⊂ R2 are considered. By applying results from complex approximation theory we obtain results on the approximation properties of special classes of solutions of Lu = 0 on G . These solutions are used as trial functions in a method for solving the eigenvalue problem which is based on a‐posteriori error bounds. Singular trial functions are applied to smooth the problem at corner points of G . In special situations, this method can produce approximations of eigenvalues and eigenfunctions with extremely high accuracy by only using a low number of trial functions. Some illustrative numerical examples for the eigenvalue problem with the Laplacian are presented. We discuss two problems from plasma physics (‘relaxed plasma’, ‘MHD‐equation’).
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DOI: 10.1002/zamm.200310081
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