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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Finite elements on degenerate meshes: inverse-type inequalities and applications
Ivan G. Graham, Wolfgang Hackbusch and Stefan A. SauterAbstract
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.
- Received:
- 27.11.02
- Published:
- 27.11.02
- Keywords:
- finite elements, degenerate meshes, graded meshes