Nonconforming tetrahedral finite elements for fourth order elliptic equations

Ming Wang, Xu Jinchao

Research output: Contribution to journalArticlepeer-review

24 Scopus citations

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 bi-harmonic 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.

Original languageEnglish (US)
Pages (from-to)1-18
Number of pages18
JournalMathematics of Computation
Volume76
Issue number257
DOIs
StatePublished - Jan 2007

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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