@article{1f6e3209c6bd4cbaa2faf08b7aae6ee9,
title = "Approximation theory methods for solving elliptic eigenvalue problems",
abstract = "Eigenvalue problems with elliptic operators L on a domain G C 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).",
keywords = "METIS-214127, Elliptic eigenvalue problems, Complex approximation, A-posteriori error bounds, Defect-minimization method, Degree of approximation",
author = "Still, {Georg J.}",
year = "2003",
doi = "10.1002/zamm.200310081",
language = "English",
volume = "83",
pages = "468--478",
journal = "Zeitschrift f{\"u}r angewandte Mathematik und Mechanik",
issn = "0044-2267",
publisher = "Wiley-VCH Verlag",
number = "7",
}