A Family Of 3d Continuously Differentiable Finite Elementsrnon Tetrahedral Grids

摘要

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 Zenisek. A mathematical justification and numerical tests are presented.rnThe current 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.