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Piecewise divergence-free discontinuous Galerkin methods for Stokes flow
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
Umeå University.
2008 (English)In: Communications in Numerical Methods in Engineering, ISSN 1069-8299, E-ISSN 1099-0887, Vol. 24, no 5, 355-366 p.Article in journal (Refereed) Published
Abstract [en]

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 C-0 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.

Place, publisher, year, edition, pages
2008. Vol. 24, no 5, 355-366 p.
Keyword [en]
solenoidal elements, Stokes problem, stream function, discontinuous Galerkin
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15824DOI: 10.1002/cnm.975ISI: 000256408000002OAI: oai:DiVA.org:hj-15824DiVA: diva2:440327
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2012-02-07Bibliographically approved

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Hansbo, Peter
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