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A unified stabilized method for Stokes' and Darcy's equations
Ecole Polytechnique Fédérale de Lausanne.
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
2007 (English)In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 198, no 1, p. 35-51Article in journal (Refereed) Published
Abstract [en]

We use the lowest possible approximation order, piecewise linear, continuous velocities and piecewise constant pressures to compute solutions to Stokes equation and Darcy's equation, applying an edge stabilization term to avoid locking. We prove that the formulation satisfies the discrete inf-sup condition, we prove an optimal a priori error estimate for both problems. The formulation is then extended to the coupled case using a Nitsche-type weak formulation allowing for different meshes in the two subdomains. Finally, we present some numerical examples verifying the theoretical predictions and showing the flexibility of the coupled approach.

Place, publisher, year, edition, pages
2007. Vol. 198, no 1, p. 35-51
Keywords [en]
Stokes' equation, Darcy's equation, stabilized methods, finite element, interior penalty method, Nitsche's method, domain decomposition, inf-sup condition
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15826DOI: 10.1016/j.cam.2005.11.022ISI: 000241177100003OAI: oai:DiVA.org:hj-15826DiVA, id: diva2:440326
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2017-12-08Bibliographically approved

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Hansbo, Peter

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