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Edge stabilization for the generalized Stokes problem: a continuous interior penalty method
journal contribution
posted on 2023-06-07, 22:15 authored by Erik Burman, Peter HansboIn this note we introduce and analyze a stabilized finite element method for the generalized Stokes equation. Stability is obtained by adding a least squares penalization of the gradient jumps across element boundaries. The method can be seen as a higher order version of the BrezziPitkranta penalty stabilization [F. Brezzi, J. Pitkranta, On the stabilization of finite element approximations of the Stokes equations, in: W. Hackbusch (Ed.), Efficient Solution of Elliptic Systems, Vieweg, 1984], but gives better resolution on the boundary for the Stokes equation than does classical Galerkin least-squares formulation. We prove optimal and quasi-optimal convergence properties for Stokes problem and for the porous media models of Darcy and Brinkman. Some numerical examples are given.
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Publication status
- Published
Journal
Computer Methods in Applied Mechanics and EngineeringISSN
0045-7825External DOI
Issue
19-22Volume
195Page range
2393-2410Department affiliated with
- Mathematics Publications
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- No
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- Yes
Legacy Posted Date
2012-02-06Usage metrics
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