A family of 3D continuously differentiable finite elements on tetrahedral grids

A family of continuously differentiable piecewise polynomials of degree 9 and higher, on general tetrahedral grids, is constructed, by simplifying and extending the P 9 element of Ženišek. A mathematical justification and numerical tests are presented. rrent computing power is still limited for the computation with 3D C 1 finite elements in general. The construction here mainly serves the purposes of understanding and ensuring the approximation properties of C 1 finite elements spaces on tetrahedral grids. In particular, this construction indicates that the 3D divergence-free C 0 - P k elements have the full order of approximation for any degree k ⩾ 8 .