  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 Gau{\ss}-Seidel iteration for solving the global
error problem prove sufficient to provide directional information necessary for
successful mesh adaptation. .
