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

Published online by Cambridge University Press:  15 November 2005

Vivette Girault
Affiliation:
Université Pierre et Marie Curie, Paris VI, Laboratoire Jacques-Louis Lions, , place Jussieu, 75252 Paris Cedex 05, France. girault@ann.jussieu.fr
Béatrice Rivière
Affiliation:
Department of Mathematics, University of Pittsburgh, 301 Thackeray, Pittsburgh, PA 15260, USA. riviere@math.pitt.edu
Mary F. Wheeler
Affiliation:
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
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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.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2005

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