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Volume 17,     Number 3,     Fall 2009

 

ANISOTROPIC MESH ADAPTATION FOR
VARIATIONAL PROBLEMS USING
ERROR ESTIMATION BASED ON
HIERARCHICAL BASES
WEIZHANG HUANG, LENNARD KAMENSKI AND XIANPING LI

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.

 

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