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


Reference:

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

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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.

Details

Item Type Articles
CreatorsGraham, I. G., Hackbusch, W. and Sauter, S. A.
DOI10.1093/imanum/drh017
DepartmentsFaculty of Science > Mathematical Sciences
RefereedYes
StatusPublished
ID Code7153
Additional InformationID number: ISI:000227771000007

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