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family of continuously differentiable finite elements on simplicial grids in four space dimensions Shangyou Zhang∗ A family of continuously differentiable piecewise polynomials of degree k, for all k ≥ 17, on general 4D simplicial grids, is constructed. Such a finite element space assumes full order of approximation. As a byproduct, we obtain a family of special 3D C2-Pk elements on tetrahedral grids