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V. Heuveline, R. Rannacher

Duality-based adaptivity in the hp-finite element method

Keywords: hp-finite element method, a posteriori error analysis, Adaptivity, error control, DWR method

In this paper a duality-based a posteriori error analysis is developed for the conforming hp Galerkin finite element approximation of second-order elliptic problems. Duality arguments combined with Galerkin orthogonality yield representations of the error in arbitrary quantities of interest. From these error estimates, criteria are derived for the simultaneous adaptation of the mesh size h and the polynomial degree p. The effectivity of this procedure is confirmed by numerical tests.

Journal of Numerical Mathematics, Walter de Gruyter

Print ISSN: 1570-2820
Volume: 11, 06/2003
Pages: 95 - 113

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