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Continuous interior penalty finite element method for Oseen's equations
Jönköping University, School of Engineering, JTH. Research area Product Development - Simulation and Optimization.
2006 (English)In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 44, no 3, 1248-1274 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we present an extension of the continuous interior penalty method of Douglas and Dupont [ Interior penalty procedures for elliptic and parabolic Galerkin methods, in Computing Methods in Applied Sciences, Lecture Notes in Phys. 58, Springer-Verlag, Berlin, 1976, pp. 207 - 216] to Oseen's equations. The method consists of a stabilized Galerkin formulation using equal order interpolation for pressure and velocity. To counter instabilities due to the pressure/ velocity coupling, or due to a high local Reynolds number, we add a stabilization term giving L-2-control of the jump of the gradient over element faces ( edges in two dimensions) to the standard Galerkin formulation. Boundary conditions are imposed in a weak sense using a consistent penalty formulation due to Nitsche. We prove energy-type a priori error estimates independent of the local Reynolds number and give some numerical examples recovering the theoretical results.

Place, publisher, year, edition, pages
2006. Vol. 44, no 3, 1248-1274 p.
Keyword [en]
finite element methods, stabilized methods, continuous interior penalty, Oseen's equations
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hj:diva-15827DOI: 10.1137/040617686ISI: 000239038700016OAI: oai:DiVA.org:hj-15827DiVA: diva2:440325
Available from: 2011-09-12 Created: 2011-08-16 Last updated: 2012-02-06Bibliographically approved

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