Continuous interior penalty finite element method for Oseen's equations
Journal article, 2006

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.

finite element methods

stabilized methods

Oseen's equations

continuous interior penalty


Erik Burman

Swiss Federal Institute of Technology in Lausanne (EPFL)

Miguel Fernandez

Institut National de Recherche en Informatique et en Automatique (INRIA)

Peter F G Hansbo

Chalmers, Applied Mechanics, Computational Technology

SIAM Journal on Numerical Analysis

0036-1429 (ISSN) 1095-7170 (eISSN)

Vol. 44 3 1248 - 1274

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics



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