Header

UZH-Logo

Maintenance Infos

FEM for elliptic eigenvalue problems: how coarse can the coarsest mesh be chosen? An experimental study


Banjai, L; Börm, S; Sauter, S (2008). FEM for elliptic eigenvalue problems: how coarse can the coarsest mesh be chosen? An experimental study. Computing and Visualization in Science, 11(4-6):363-372.

Abstract

In this paper, we consider the numerical discretization of elliptic eigenvalue problems by Finite Element Methods and its solution by a multigrid method. From the general theory of finite element and multigrid methods, it is well known that the asymptotic convergence rates become visible only if the mesh width h is sufficiently small, h ≤ h 0. We investigate the dependence of the maximal mesh width h 0 on various problem parameters such as the size of the eigenvalue and its isolation distance. In a recent paper (Sauter in Finite elements for elliptic eigenvalue problems in the preasymptotic regime. Technical Report. Math. Inst., Univ. Zürich, 2007), the dependence of h 0 on these and other parameters has been investigated theoretically. The main focus of this paper is to perform systematic experimental studies to validate the sharpness of the theoretical estimates and to get more insights in the convergence of the eigenfunctions and -values in the preasymptotic regime.

Abstract

In this paper, we consider the numerical discretization of elliptic eigenvalue problems by Finite Element Methods and its solution by a multigrid method. From the general theory of finite element and multigrid methods, it is well known that the asymptotic convergence rates become visible only if the mesh width h is sufficiently small, h ≤ h 0. We investigate the dependence of the maximal mesh width h 0 on various problem parameters such as the size of the eigenvalue and its isolation distance. In a recent paper (Sauter in Finite elements for elliptic eigenvalue problems in the preasymptotic regime. Technical Report. Math. Inst., Univ. Zürich, 2007), the dependence of h 0 on these and other parameters has been investigated theoretically. The main focus of this paper is to perform systematic experimental studies to validate the sharpness of the theoretical estimates and to get more insights in the convergence of the eigenfunctions and -values in the preasymptotic regime.

Statistics

Citations

Altmetrics

Downloads

24 downloads since deposited on 05 Jan 2009
1 download since 12 months
Detailed statistics

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:September 2008
Deposited On:05 Jan 2009 13:53
Last Modified:06 Dec 2017 15:45
Publisher:Springer
ISSN:1432-9360
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00791-008-0101-5
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2425502

Download