The Morley element for fourth order elliptic equations in any dimensions

Wang Ming, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

65 Scopus citations

Abstract

In this paper, the well-known nonconforming Morley element for biharmonic equations in two spatial dimensions is extended to any higher dimensions in a canonical fashion. The general n-dimensional Morley element consists of all quadratic polynomials defined on each n-simplex with degrees of freedom given by the integral average of the normal derivative on each (n-1)-subsimplex and the integral average of the function value on each (n-2)-subsimplex. Explicit expressions of nodal basis functions are also obtained for this element on general n-simplicial grids. Convergence analysis is given for this element when it is applied as a nonconforming finite element discretization for the biharmonic equation.

Original languageEnglish (US)
Pages (from-to)155-169
Number of pages15
JournalNumerische Mathematik
Volume103
Issue number1
DOIs
StatePublished - Mar 1 2006

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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