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Edge stabilization for the generalized Stokes problem: A continuous interior penalty method

Erik Burman ; Peter Hansbo (Institutionen för tillämpad mekanik, Beräkningsteknik)
Computer Methods in Applied Mechanics and Engineering Vol. 195 (2006), 19-22, p. 2393-2410.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Generalized Stokes equation, Stabilized methods, Finite element, Interior penalty method, Gradient jumps, Inf-sup condition



Denna post skapades 2007-01-09.
CPL Pubid: 19885

 

Institutioner (Chalmers)

Institutionen för tillämpad mekanik, Beräkningsteknik (2005-2006)

Ämnesområden

Numerisk analys
Strömningsmekanik

Chalmers infrastruktur