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 FEMAveraging 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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