A family of higher order mixed finite element methods for plane elasticity

Douglas N. Arnold, Jim Douglas, Chaitan P. Gupta

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168 Scopus citations

Abstract

The Dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the Raviart-Thomas mixed finite elements for a scalar, second-order elliptic equation. Estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor in L2(Ω), and optimal order negative norm estimates are obtained in Hs(Ω)′ for a range of s depending on the index of the finite element space. An optimal order estimate in L(Ω) for the displacement error is given. Also, a quasioptimal estimate is derived in an appropriate space. All estimates are valid uniformly with respect to the compressibility and apply in the incompressible case. The formulation of the elements is presented in detail.

Original languageEnglish (US)
Pages (from-to)1-22
Number of pages22
JournalNumerische Mathematik
Volume45
Issue number1
DOIs
StatePublished - Feb 1 1984

Keywords

  • Subject Classifications: AMS(MOS): 65N30, CR: G 1.8

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