Adaptive finite elements with anisotropic meshes

Details Adaptive finite elements with anisotropic meshes Adaptive finite elements with anisotropic meshes

2012-01-19

arxiv.org/abs/1201.4090v2

Mathematics

Numerical Analysis

10 pages, 4 figures, revised introduction

Scientific paper

The paper presents a numerical study for the finite element method with anisotropic meshes. We compare the accuracy of the numerical solutions on quasi-uniform, isotropic, and anisotropic meshes for a test problem which combines several difficulties of a corner singularity, a peak, a boundary layer, and a wavefront. Numerical experiment clearly shows the advantage of anisotropic mesh adaptation. The conditioning of the resulting linear equation system is addressed as well. In particular, it is shown that the conditioning with adaptive anisotropic meshes is not as bad as generally assumed.

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