Piecewise divergence free discontinuous Galerkin methods

Hansbo, Peter F G,1959Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology (författare)

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.

Larson, Mats G,1968Umeå universitet,Umeå University(Swepub:cth)mgl (författare)
Göteborgs universitetInstitutionen för matematiska vetenskaper, matematik (creator_code:org_t)

Ingår i:Communications in Numerical Methods in Engineering: Wiley24:5, s. 355-3661069-82991099-0887

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