Finite element basis functions for nested meshes of nonuniform refinement level

We propose a systematic methodology for the construction of hanging variables to connect finite elements of unequal refinement levels within a nested tetrahedral 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. This paper covers H¹ and H(curl) basis functions for triangular or tetrahedral elements.