Anisotropic mesh adaptation for variational problems using error estimation based on hierarchical bases

Abstract

Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial dierential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error estimator for the development of an anisotropic metric tensor needed for the adaptive nite element solution of variational problems. The new metric tensor is completely a posteriori and based on residual, edge jumps and the hierarchical basis error estimator. Numerical results show that it performs comparable with existing metric tensors based on Hessian recovery. A few sweeps of the symmetric Gau-Seidel iteration for solving the global error problem prove sucient to provide directional information necessary for successful mesh adaptation.