99-11   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Carsten Carstensen, Sören Bartels:

Each Averaging Technique Yields Reliable A~Posteriori Error Control in FEM on Unstructured Grids Part I: Low Order Conforming, Nonconforming, and Mixed FEM

Averaging techniques are popular tools in adaptive finite element methods for the numerical treatment of second order partial differential equations since they provide efficient a~posteriori error estimates by a simple postprocessing. In this paper, their reliablility is shown for conforming, nonconforming, and mixed low 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 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, 73C5

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


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