Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases
Year: 2010
Type: preprint
Abstract: Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential 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 finite 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 Gauß-Seidel iteration for solving the global error problem prove sufficient to provide directional information necessary for successful mesh adaptation. .
Source: arXiv (Cornell University)
Institution: University of Kansas
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1561407954