Header

UZH-Logo

Maintenance Infos

Finite elements on degenerate meshes: inverse-type inequalities and applications


Graham, I; Hackbusch, W; Sauter, S (2005). Finite elements on degenerate meshes: inverse-type inequalities and applications. IMA Journal of Numerical Analysis, 25(2):379-407.

Abstract

In this paper we obtain a range of inverse-type inequalities which are applicable to finite-element functions on general classes of meshes, including degenerate meshes obtained by anisotropic refinement. These are obtained for Sobolev norms of positive, zero and negative order. In contrast to classical inverse estimates, negative powers of the minimum mesh diameter are avoided. We give two applications of these estimates in the context of boundary elements: (i) to the analysis of quadrature error in discrete Galerkin methods and (ii) to the analysis of the panel clustering algorithm. Our results show that degeneracy in the meshes yields no degradation in the approximation properties of these methods.

Abstract

In this paper we obtain a range of inverse-type inequalities which are applicable to finite-element functions on general classes of meshes, including degenerate meshes obtained by anisotropic refinement. These are obtained for Sobolev norms of positive, zero and negative order. In contrast to classical inverse estimates, negative powers of the minimum mesh diameter are avoided. We give two applications of these estimates in the context of boundary elements: (i) to the analysis of quadrature error in discrete Galerkin methods and (ii) to the analysis of the panel clustering algorithm. Our results show that degeneracy in the meshes yields no degradation in the approximation properties of these methods.

Statistics

Citations

35 citations in Web of Science®
35 citations in Scopus®
Google Scholar™

Altmetrics

Downloads

36 downloads since deposited on 03 Mar 2010
4 downloads 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
Uncontrolled Keywords:finite elements; degenerate meshes; boundary element method; quadrature; panel-clustering
Language:English
Date:2005
Deposited On:03 Mar 2010 10:54
Last Modified:05 Apr 2016 13:24
Publisher:Oxford University Press
ISSN:0272-4979
Additional Information:This is a pre-copy-editing, author-produced PDF of an article accepted for publication in [IMA Journal of Numerical Analysis] following peer review. The definitive publisher-authenticated version [Finite elements on degenerate meshes: Inverse-type inequalities and applications (2005) IMA Journal of Numerical Analysis, 25 (2), pp. 379-407] is available online at: http://imajna.oxfordjournals.org/cgi/content/abstract/25/2/379
Publisher DOI:https://doi.org/10.1093/imanum/drh017

Download

Preview Icon on Download
Preview
Filetype: PDF
Size: 1MB
View at publisher