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Continuous interior penalty finite element method for Oseen's equations
journal contribution
posted on 2023-06-07, 21:15 authored by Erik Burman, Miguel A Fernández, Peter HansboIn 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.
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Publication status
- Published
Journal
SIAM Journal on Numerical AnalysisISSN
0036-1429Publisher
Society for Industrial and Applied MathematicsExternal DOI
Issue
3Volume
44Page range
1248-1274Pages
27.0Department affiliated with
- Mathematics Publications
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- No
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- Yes
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2012-02-06Usage metrics
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