Adaptive finite elements with anisotropic meshes

Abstract

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.

10 pages, 4 figures, revised introduction

References in corpus (4)

• A new anisotropic mesh adaptation method based upon hierarchical a posteriori error estimates
• Conditioning of Finite Element Equations with Arbitrary Anisotropic Meshes
• Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases
• A Study on Using Hierarchical Basis Error Estimates in Anisotropic Mesh Adaptation for the Finite Element Method