Divergence-free HDG methods for the vorticity-velocity formulation of the stokes problem

Bernardo Cockburn, Jintao Cui

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study a hybridizable discontinuous Galerkin method for solving the vorticity-velocity formulation of the Stokes equations in three-space dimensions. We show how to hybridize the method to avoid the construction of the divergence-free approximate velocity spaces, recover an approximation for the pressure and implement the method efficiently. We prove that, when all the unknowns use polynomials of degree k≥0, the L 2 norm of the errors in the approximate vorticity and pressure converge with order k+1/2 and the error in the approximate velocity converges with order k+1. We achieve this by letting the normal stabilization function go to infinity in the error estimates previously obtained for a hybridizable discontinuous Galerkin method.

Original languageEnglish (US)
Pages (from-to)256-270
Number of pages15
JournalJournal of Scientific Computing
Volume52
Issue number1
DOIs
StatePublished - Jul 2012

Bibliographical note

Funding Information:
The first author was partially supported by the National Science Foundation (Grant DMS-0712955) and by the Minnesota Supercomputing Institute.

Keywords

  • Discontinuous Galerkin methods
  • Hybridization
  • Incompressible fluid flow

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