Piecewise divergence free discontinuous Galerkin methods
Journal article, 2008

In this paper, we consider different possibilities of using divergence-free discontinuous Galerkin methods for the Stokes problem in order to eliminate the pressure from the discrete problem. We focus on three different approaches: one based on a C0 approximation of the stream function in two dimensions (the vector potential in three dimensions), one based on the non-conforming Morley element (which corresponds to a divergence-free non-conforming Crouzeix-Raviart approximation of the velocities), and one fully discontinuous Galerkin method with a stabilization of the pressure that allows the edgewise elimination of the pressure variable before solving the discrete system. We limit the analysis in the stream function case to two spatial dimensions, while the analysis of the fully discontinuous approach is valid also in three dimensions.

Stokes problem

discontinuous Galerkin

stream function

solenoidal elements


Peter F G Hansbo

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Mats G Larson

Umeå University

Communications in Numerical Methods in Engineering

1069-8299 (ISSN) 1099-0887 (eISSN)

Vol. 24 5 355-366

Subject Categories

Computational Mathematics



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