We propose a systematic methodology for the construction of generalized hanging variables which can be used 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. The present paper covers higher order H~(1) and H(curl) conforming elements of hierarchical type.
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