3D $H^2$nonconforming tetrahedral finite elements for the biharmonic equation
Abstract
In this article, a family of $H^2$nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3D. In the family, the $P_\ell$ polynomial space is enriched by some high order polynomials for all $\ell\ge 3$ and the corresponding finite element solution converges at the optimal order $\ell1$ in $H^2$ norm. Moreover, the result is improved for two low order cases by using $P_6$ and $P_7$ polynomials to enrich $P_4$ and $P_5$ polynomial spaces, respectively. The optimal order error estimate is proved. The numerical results are provided to confirm the theoretical findings.
 Publication:

arXiv eprints
 Pub Date:
 September 2019
 arXiv:
 arXiv:1909.08178
 Bibcode:
 2019arXiv190908178H
 Keywords:

 Mathematics  Numerical Analysis