Continuous interior penalty finite element method for Oseen's equations

Burman, Erik, Fernández, Miguel A and Hansbo, Peter (2006) Continuous interior penalty finite element method for Oseen's equations. SIAM Journal on Numerical Analysis, 44 (3). pp. 1248-1274. ISSN 0036-1429

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Abstract

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 L2-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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Erik Burman
Date Deposited: 06 Feb 2012 18:45
Last Modified: 20 Jun 2012 14:39
URI: http://sro.sussex.ac.uk/id/eprint/18181
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