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Anisotropic mesh adaptation has been successfully applied to the numericalsolution of partial differential equations but little considered forvariational problems. In this paper, we investigate the use of a globalhierarchical basis error estimator for the development of an anisotropic metrictensor needed for the adaptive finite element solution of variational problems.The new metric tensor is completely a~posteriori and based on residual, edgejumps and the hierarchical basis error estimator. Numerical results show thatit performs comparable with existing metric tensors based on Hessian recovery.A few sweeps of the symmetric Gau{\ss}-Seidel iteration for solving the globalerror problem prove sufficient to provide directional information necessary forsuccessful mesh adaptation. .

Anisotropic Mesh Adaptation for Variational Problems Using Error Estimation Based on Hierarchical Bases