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A family of 3D H2-nonconforming tetrahedral finite elements for the biharmonic equation

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Abstract

In this article, a family of H2-nonconforming finite elements on tetrahedral grids is constructed for solving the biharmonic equation in 3D. 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.

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Acknowledgements

The first author was supported by National Natural Science Foundation of China (Grant Nos. 11625101 and 11421101).

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Authors and Affiliations

  1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Jun Hu & Shudan Tian

  2. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, USA

    Shangyou Zhang

Authors
  1. Jun Hu
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  2. Shudan Tian
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  3. Shangyou Zhang
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Correspondence to Shudan Tian.

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Hu, J., Tian, S. & Zhang, S. A family of 3D H2-nonconforming tetrahedral finite elements for the biharmonic equation. Sci. China Math. 63, 1505–1522 (2020). https://doi.org/10.1007/s11425-019-1661-8

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  • DOI: https://doi.org/10.1007/s11425-019-1661-8

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