Convergence of an adaptive hp finite element strategy in one space dimension

Authors:
W. Dörfler;V. Heuveline
Affiliations:
Institut für Angewandte und Numerische Mathematik 2, Universität Karlsruhe, 76128 Karlsruhe, Germany;Institut für Angewandte und Numerische Mathematik 2, Universität Karlsruhe, 76128 Karlsruhe, Germany
Venue:
Applied Numerical Mathematics
Year:
2007

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Abstract

We show uniform decrease in energy error for an hp-adaptive algorithm with automatic hp selection on the elliptic model boundary value problem. The result is based on a new marking strategy for the finite element refinement. In case of a solution with algebraic singularity we demonstrate that we achieve the known theoretical optimal error behavior.