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Article Dans Une Revue SIAM Journal on Numerical Analysis Année : 2006

Continuous Interior Penalty Finite Element Method for Oseen's Equations

Résumé

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 pres-sure/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.
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Dates et versions

hal-01345519 , version 1 (13-07-2016)

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Paternité

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Erik Burman, Miguel Angel Fernández, Peter Hansbo. Continuous Interior Penalty Finite Element Method for Oseen's Equations. SIAM Journal on Numerical Analysis, 2006, 44 (3), pp.1248-1274. ⟨10.1137/040617686⟩. ⟨hal-01345519⟩
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