Abstract
In many applications of the finite element method, the explicit form of the basis functions is not known. A well-known exception is that of piecewise linear approximation over a triangulation of the plane, where the basis functions are pyramid functions. In the present paper, the basis functions are displayed in closed form for piecewise polynomial approximation of degreen over a triangulation of the plane. These basis functions are expressed simply in terms of the pyramid functions for linear approximation.
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Mitchell, A.R., Phillips, G.M. Construction of basis functions in the finite element method. BIT 12, 81–89 (1972). https://doi.org/10.1007/BF01932676
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DOI: https://doi.org/10.1007/BF01932676