Journal of Scientific Computing

, Volume 40, Issue 1, pp 188-210

First online:

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

  • Bernardo CockburnAffiliated withSchool of Mathematics, University of Minnesota
  • , Guido KanschatAffiliated withDepartment of Mathematics, Texas A&M University
  • , Dominik SchötzauAffiliated withMathematics Department, University of British Columbia Email author 

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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.


Discontinuous Galerkin methods Equal-order methods Incompressible Navier-Stokes equations