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Inverse-type estimates on hp-finite element spaces and applications

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posted on 2009-12-08, 16:13 authored by Emmanuil H. Georgoulis
This work is concerned with the development of inverse-type inequalities for piecewise polynomial functions and, in particular, functions belonging to hp-finite element spaces. The cases of positive and negative Sobolev norms are considered for both continuous and discontinuous finite element functions. The inequalities are explicit both in the local polynomial degree and the local mesh size. The assumptions on the hp-finite element spaces are very weak, allowing anisotropic (shape-irregular) elements and varying polynomial degree across elements. Finally, the new inverse-type inequalities are used to derive bounds for the condition number of symmetric stiffness matrices of hp-boundary element method discretisations of integral equations, with element-wise discontinuous basis functions constructed via scaled tensor products of Legendre polynomials.

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Citation

Mathematics of Computation, 2008, 77 (261), pp. 201-219

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  • VoR (Version of Record)

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Mathematics of Computation

Publisher

American Mathematical Society

issn

0025-5718

Available date

2009-12-08

Publisher version

http://www.ams.org/journals/mcom/2008-77-261/S0025-5718-07-02068-6/home.html

Language

en

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