Local discontinuous Galerkin methods for the stokes system

Bernardo Cockburn, Guido Kanschat, Dominik Schötzau, Christoph Schwab

Research output: Contribution to journalArticlepeer-review

174 Scopus citations

Abstract

In this paper, we introduce and analyze local discontinuous Galerkin methods for the Stokes system. For a class of shape regular meshes with hanging nodes we derive a priori estimates for the L2-norm of the errors in the velocities and the pressure. We show that optimal-order estimates are obtained when polynomials of degree k are used for each component of the velocity and polynomials of degree k - 1 for the pressure, for any k ≥ 1. We also consider the case in which all the unknowns are approximated with polynomials of degree k and show that, although the orders of convergence remain the same, the method is more efficient. Numerical experiments verifying these facts are displayed.

Original languageEnglish (US)
Pages (from-to)319-343
Number of pages25
JournalSIAM Journal on Numerical Analysis
Volume40
Issue number1
DOIs
StatePublished - Apr 2002

Keywords

  • Discontinuous Galerkin methods
  • Finite elements
  • Stokes system

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