Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions

Bernardo Cockburn, Guosheng Fu

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

We propose a new tool, which we call M-decompositions, for devising superconvergent hybridizable discontinuous Galerkin (HDG) methods and hybridized-mixed methods for linear elasticity with strongly symmetric approximate stresses on unstructured polygonal/polyhedral meshes. We show that for an HDG method, when its local approximation space admits an M-decomposition, optimal convergence of the approximate stress and superconvergence of an element-by-element postprocessing of the displacement field are obtained. The resulting methods are locking-free. Moreover, we explicitly construct approximation spaces that admit M-decompositions on general polygonal elements.We display numerical results on triangular meshes validating our theoretical findings.

Original languageEnglish (US)
Pages (from-to)566-604
Number of pages39
JournalIMA Journal of Numerical Analysis
Volume38
Issue number2
StatePublished - Apr 18 2018

Keywords

  • discontinuous Galerkin
  • hybridizable
  • linear elasticity
  • strong symmetry
  • superconvergence

Fingerprint Dive into the research topics of 'Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions'. Together they form a unique fingerprint.

Cite this