Journal of Scientific Computing

, Volume 40, Issue 1, pp 188–210

An Equal-Order DG Method for the Incompressible Navier-Stokes Equations

  • Bernardo Cockburn
  • Guido Kanschat
  • Dominik Schötzau
Article

DOI: 10.1007/s10915-008-9261-1

Cite this article as:
Cockburn, B., Kanschat, G. & Schötzau, D. J Sci Comput (2009) 40: 188. doi:10.1007/s10915-008-9261-1

Abstract

We introduce and analyze a discontinuous Galerkin method for the incompressible Navier-Stokes equations that is based on finite element spaces of the same polynomial order for the approximation of the velocity and the pressure. Stability of this equal-order approach is ensured by a pressure stabilization term. A simple element-by-element post-processing procedure is used to provide globally divergence-free velocity approximations. For small data, we prove the existence and uniqueness of discrete solutions and carry out an error analysis of the method. A series of numerical results are presented that validate our theoretical findings.

Keywords

Discontinuous Galerkin methodsEqual-order methodsIncompressible Navier-Stokes equations

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Bernardo Cockburn
    • 1
  • Guido Kanschat
    • 2
  • Dominik Schötzau
    • 3
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of MathematicsTexas A&M UniversityCollege StationUSA
  3. 3.Mathematics DepartmentUniversity of British ColumbiaVancouverCanada