Edge stabilization for the generalized Stokes problem: A continuous interior penalty method
Journal article, 2006

In 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 Brezzi–Pitkäranta penalty stabilization [F. Brezzi, J. Pitkäranta, 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.

Inf-sup condition

Stabilized methods

Gradient jumps

Interior penalty method

Finite element

Generalized Stokes equation


Erik Burman

Peter F G Hansbo

Chalmers, Applied Mechanics, Computational Technology

Computer Methods in Applied Mechanics and Engineering

Vol. 195 19-22 2393-2410

Subject Categories

Computational Mathematics

Fluid Mechanics and Acoustics

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