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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.
Key Words: hp-finite element method,; a posteriori error analysis,; adaptivity,; error control,; DWR method
Published Online: 2003-06-01
Published in Print: 2003-06-01
Copyright 2003, Walter de Gruyter
