00-5   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Sören Bartels, Carsten Carstensen:

Each Averaging Technique Yields Reliable A Posteriori Error Control in FEM on Unstructured Grids. Part II: Higher Order FEM

Averaging techniques are popular tools in adaptive finite element methods since they provide efficient a~posteriori error estimates by a simple postprocessing. In the second paper of our analysis of their reliability, we consider conforming $h$-FEM of higher (i.e., not of lowest) order in two or three space dimensions. In this paper, reliablility is shown for conforming higher order finite element methods in a model situation, the Laplace equation with mixed boundary conditions. Emphasis is on possibly unstructured grids, non-smoothness of exact solutions, and a wide class of local averaging techniques. Theoretical and numerical evidence supports that the reliability is up to the smoothness of given right-hand sides.

Mathematics Subject Classification (1991): 65N30, 65R20, 73C50

Keywords: a posteriori error estimates, residual based error estimate, adaptive algorithm, reliability, finite element method, higher order finite element method

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