Research Article

A splitting method using discontinuous Galerkin for the transient incompressible Navier-Stokes equations

Girault, Vivette^a1, Rivière, Béatrice^a2 and Wheeler, Mary F.^a3

^a1 Université Pierre et Marie Curie, Paris VI, Laboratoire Jacques-Louis Lions, , place Jussieu, 75252 Paris Cedex 05, France. girault@ann.jussieu.fr

^a2 Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, PA 15260, USA. riviere@math.pitt.edu

^a3 Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, University of Texas, 201 E. 24th St., Austin TX 78712, USA. mfw@ices.utexas.edu

Abstract

In this paper we solve the time-dependent incompressible Navier-Stokes equations by splitting the non-linearity and incompressibility, and using discontinuous or continuous finite element methods in space. We prove optimal error estimates for the velocity and suboptimal estimates for the pressure. We present some numerical experiments.

(Received September 1 2004)

(Online publication November 15 2005)

Key Words:

• Operator splitting;
• time-dependent Navier-Stokes;
• SIPG.

Mathematics Subject Classification:

• 65M12;
• 65M15;
• 65M60