3D H^2-nonconforming tetrahedral finite elements for the biharmonic equation
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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_ℓ polynomial space is enriched by some high order polynomials for all ℓ> 3 and the corresponding finite element solution converges at the optimal order ℓ-1 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.
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