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- Title
An optimal order numerical quadrature approximation of a planar isoparametric eigenvalue problem on triangular finite element meshes.
- Authors
Andreev, A. B.; Petrov, M. S.; Todorov, T. D.
- Abstract
This paper deals with a finite element numerical quadrature method. It is applied for a class of second-order self-adjoint elliptic operators defined on a bounded domain in the plane. Isoparametric finite element transformations and triangular Lagrange finite elements are used. We establish the rate of convergence for approximate eigenvalues and eigenfunctions of second-order elliptic eigenvalue problems, obtained by a numerical quadrature finite element approximation. Thus the relationship between possible quadrature formulas and the optimal and almost optimal precision of the method is established. The emphasis of the paper is on the error analysis of the approximate eigenpairs. Numerical results confirming the theory are presented.
- Subjects
APPROXIMATION theory; EIGENVALUES; MATRICES (Mathematics); FINITE element method; NUMERICAL analysis; MATHEMATICAL transformations
- Publication
Calcolo, 2005, Vol 42, Issue 2, p47
- ISSN
0008-0624
- Publication type
Article
- DOI
10.1007/s10092-005-0097-x