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Polygonal finite elements

A new class of finite element basis functions for arbitrary polygons is presented. The approximation spaces fulfill the same commuting properties as the standard Whitney approximation spaces. An example for the application of the new basis functions to a standard problem formulated with the finite integration technique (FIT) or the finite element method is given. The special choice of elements in the example suggests a rigorous implementation of subgridding in FIT/finite-difference time-domain schemes