Burman, E;
Fernandez, MA;
Hansbo, P;
(2006)
Continuous Interior Penalty Finite Element Method for Oseen's Equations.
SIAM Journal on Numerical Analysis
, 44
(3)
pp. 1248-1274.
10.1137/040617686.
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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.
| Type: | Article |
|---|---|
| Title: | Continuous Interior Penalty Finite Element Method for Oseen's Equations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1137/040617686 |
| Publisher version: | http://dx.doi.org/10.1137/040617686 |
| Language: | English |
| Additional information: | Copyright © 2006 Society for Industrial and Applied Mathematics |
| Keywords: | finite element methods, stabilized methods, continuous interior penalty, Oseen's equations |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1384735 |
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