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Piecewise divergence free discontinuous Galerkin methods

Peter Hansbo (Institutionen för matematiska vetenskaper, matematik) ; Mats G. Larson
Communications in Numerical Methods in Engineering (1069-8299). Vol. 24 (2008), 5, p. 355-366.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: solenoidal elements, Stokes problem, stream function, discontinuous Galerkin



Denna post skapades 2008-07-30. Senast ändrad 2016-09-07.
CPL Pubid: 72592

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Tillämpad matematik

Chalmers infrastruktur