Abstracts for the Conference on
Grid Adaptivity in Computational PDEs,
Edinburgh, July 96		Next
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A posteriori error estimators on anisotropically refined meshes and local refinement of rectangular and primatic grids

K G Siebert

Institut für Angewandte Mathematik
Universität Freiburg
Herman Herder Str. 10
D 79104 Freiburg i. Br.

Abstract

Additionally to non-adaptive finite element methods there are two basic tools needed in adaptive methods. The first tool is an algorithm for local refinement of some given triangulation. We present algorithms for the local refinement of rectangular and prismatic grids by repeated horizontal and vertical bisection.

The second tool we need is an a-posteriori error estimator. Using the information generated by such an error estimator the refinement of the grid is controlled. For 2nd order elliptic problems we present error estimators on anisotropically refined $n$-D rectangular and 3-D primatic grids that will give valid information about the size of the error; additionally it generates information about the direction in which some element has to be refined (for 2-D rectangular and 3-D primatic grids we will get the information to refine an element horizontally or vertically or isotropically).

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