Analysis of a class of nonconforming finite elements forcrystalline microstructures

Petr Klouček, Bo Li, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

An analysis is given for a class of nonconforming Lagrange-type finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed in 1992 by Rannacher and Turek for the Stokes equation. Our analysis highlights the features of these elements which make them effective for the computation of microstructure. New results for superconvergence and numerical quadrature are also given.

Original languageEnglish (US)
Pages (from-to)1111-1135
Number of pages25
JournalMathematics of Computation
Volume65
Issue number215
DOIs
StatePublished - Jul 1996

Keywords

  • Error estimate
  • Nonconforming finite element
  • Numerical quadrature
  • Superconvergence

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