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Continuous interior penalty finite element method for Oseen's equations

Erik Burman ; Miguel Fernandez ; Peter Hansbo (Institutionen för tillämpad mekanik, Beräkningsteknik)
SIAM Journal on Numerical Analysis (ISSN: 0036-1429). Vol. 44 (2006), 3, p. 1248 - 1274.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: finite element methods, stabilized methods, continuous interior penalty, Oseen's equations

Denna post skapades 2007-01-09.
CPL Pubid: 21971


Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Beräkningsteknik (2005-2006)


Numerisk analys

Chalmers infrastruktur