A family of 3D H^2-nonconforming tetrahedral finite elements for the biharmonic equation

In this article,a family of H^2-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3 D.In the family,the Pl polynomial space is enriched by some high order polynomials for all l≥3 and the corresponding finite element solution converges at the order l-1 in H2 norm.Moreover,the result is improved for two low order cases by using P6 and P7 polynomials to enrich P4 and P5 polynomial spaces,respectively.The error estimate is proved.The numerical results are.provided to confirm the theoretical findings.