The nodal basis of C^m-P_k^(3) and C^m-P_k^(4) finite elements on tetrahedral and 4D simplicial grids
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We construct the nodal basis of C^m-P_k^(3) (k ≥ 2^3m+1) and C^m-P_k^(4) (k ≥ 2^4m+1) finite elements on 3D tetrahedral and 4D simplicial grids, respectively. C^m-P_k^(n) stands for the space of globally C^m (m≥1) and locally piecewise n-dimensional polynomials of degree k on n-dimensional simplicial grids. We prove the uni-solvency and the C^m continuity of the constructed C^m-P_k^(3) and C^m-P_k^(4) finite element spaces. A computer code is provided which generates the index set for the nodal basis of C^m-P_k^(n) finite elements on n-dimensional simplicial grids.
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