Towards practical anisotropic adaptive FEM on triangular meshes: a new refinement paradigm

摘要

Adaptive anisotropic refinement of finite element meshes allows one to reduce the computational effort required to achieve a specified accuracy of the solution of a PDE problem. We present a new approach to adaptive refinement and demonstrate that this allows one to construct algorithms which generate very flexible and efficient anisotropi-cally refined meshes, even improving the convergence order compared to adaptive isotropic refinement if the problem permits.