Adaptive Mesh Refinement using General Elements

In this paper, we describe two strategies to generate solution adaptive meshes via refinement: a face-based isotropic approach and an edge-based anisotropic approach. Both employ general polyhedral elements locally to limit the propagation of mesh refinement and are applicable to a baseline mesh with arbitrary connectivity. We discuss the basic algorithms as well as a few implementation issues. We include results from four simulations that demonstrate the strengths and weaknesses of the mesh refinement strategies. In general, the face-based isotropic refinement strategy produces good results provided an appropriate trigger is employed. The anisotropic refinement strategy produces good results provided cell edges are oriented in the direction of refinement.