A study on using hierarchical basis error estimates in anisotropic mesh adaptation for the finite element method

Abstract

A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate metric which is often based on some type of Hessian recovery. This study discusses the use of a hierarchical basis error estimator for the development of an anisotropic metric tensor needed for the adaptive finite element solution. A global hierarchical basis error estimator is employed to obtain reliable directional information. Numerical results for a selection of different applications show that the method performs comparable with existing metric tensors based on Hessian recovery and can provide even better adaptation to the solution if applied to problems with gradient jumps and steep boundary layers. © 2010 Springer-Verlag Berlin Heidelberg.