A note on the devising of superconvergent HDG methods for Stokes flow by M-decompositions

Bernardo Cockburn, Guosheng Fu, Weifeng Qiu

Research output: Contribution to journalArticlepeer-review

14 Scopus citations

Abstract

In this article, we to devise superconvergent hybridizable discontinuous Galerkin methods on unstructured polygonal/polyhedral meshes for the Stokes equations of incompressible fluid flow by using M-decompositions. We do this for two formulations of the equations, namely, for the velocity gradient- velocity-pressure formulation, and for the more difficult strain rate-velocity-pressure formulation. We also show how to locally postprocess the approximate velocity to obtain a globally divergence-free and H(div)-conforming velocity converging faster than the original approximate velocity.

Original languageEnglish (US)
Pages (from-to)730-749
Number of pages20
JournalIMA Journal of Numerical Analysis
Volume37
Issue number2
DOIs
StatePublished - Apr 1 2017

Bibliographical note

Funding Information:
National Science Foundation (Grant DMS-1522657)

Keywords

  • M-decompositions.
  • Stokes flow
  • discontinuous Galerkin
  • hybridization
  • superconvergence

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