The computation of a locally conservative stress for the continuous Galerkin method for compressible linearly elastic materials

Bernardo Cockburn, Haiying Wang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We show how to postprocess the approximate displacement given by the continuous Galerkin method for compressible linearly elastic materials to obtain an optimally convergent approximate stress that renders the method locally conservative. The postprocessing is extremely efficient as it requires the inversion of a symmetric, positive definite matrix whose condition number is independent of the mesh size. Although the new stress is not symmetric, its asymmetry can be controlled by a small term which is of the same order as that of the error of the approximate stress itself. The continuous Galerkin method is thus competitive with mixed methods providing stresses with similar convergence properties.

Original languageEnglish (US)
Pages (from-to)151-163
Number of pages13
JournalJournal of Scientific Computing
Volume36
Issue number2
DOIs
StatePublished - Aug 2008

Keywords

  • Continuous Galerkin methods
  • Linear elasticity
  • Local conservativity

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