Finite Element Basis Functions for Nested Meshes of Non-Uniform Refinement Level

摘要

We propose a systematic methodology for the construction of generalized hanging variables which can be used to connect finite dements of unequal refinement levels within a nested tetrahedra! mesh. While conventional refinement schemes introduce irregular elements at such interfaces, which must be removed when the mesh is further refined, the suggested approach keeps the discretization perfectly nested. Thanks to enhanced regularity, mesh-based methods such as refinement algorithms or intergrid transfer operators for use in multigrid solvers can be implemented in a much simpler fashion. The present paper covers higher order H~1 and H(curl) conforming elements of hierarchical type.