Edge stabilization for the generalized Stokes problem: a continuous interior penalty method. (English) Zbl 1125.76038

Summary: 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 and 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 Stokes equation than does classical Galerkin least-squares formulation. We prove optimal and quasi-optimal convergence properties for Stokes problem and for porous media models of Darcy and Brinkman. Some numerical examples are given.


76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
76S05 Flows in porous media; filtration; seepage
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