## Nonconforming tetrahedral finite elements for fourth order elliptic equations

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## Abstract:

This paper is devoted to the construction of nonconforming finite elements for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed elements include two nonconforming tetrahedral finite elements and one quasi-conforming tetrahedral element. These elements are proved to be convergent for a model biharmonic equation in three dimensions. In particular, the quasi-conforming tetrahedron element is a modified Zienkiewicz element, while the nonmodified Zienkiewicz element (a tetrahedral element of Hermite type) is proved to be divergent on a special grid.## References

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## Additional Information

**Wang Ming**- Affiliation: LMAM, School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China
- Email: mwang@math.pku.edu.cn
**Jinchao Xu**- Affiliation: The School of Mathematical Sciences, Peking University; Beijing, People’s Republic of China; and Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 228866
- Email: xu@math.psu.edu
- Received by editor(s): October 8, 2004
- Received by editor(s) in revised form: September 16, 2005
- Published electronically: August 1, 2006
- Additional Notes: The work of the first author was supported by the National Natural Science Foundation of China (10571006).

The work of the second author was supported by National Science Foundation DMS-0209479 and DMS-0215392 and the Changjiang Professorship through Peking University - © Copyright 2006 American Mathematical Society
- Journal: Math. Comp.
**76**(2007), 1-18 - MSC (2000): Primary 65N30
- DOI: https://doi.org/10.1090/S0025-5718-06-01889-8
- MathSciNet review: 2261009