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Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. (English) Zbl 1077.76037

Summary: We stabilize the nonconforming Crouzeix-Raviart element for the Darcy-Stokes problem with terms motivated by a discontinuous Galerkin approach. Convergence of the method is shown, also in the limit of vanishing viscosity. Finally, some numerical examples verifying the theoretical predictions are presented.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:

[1] Mardal, SIAM J Numer Anal 40 pp 1605– (2002)
[2] Hansbo, ESAIM Math Model Numer Anal 37 pp 63– (2003)
[3] and , Mixed and hybrid finite element methods, Springer-Verlag, 1991. · Zbl 0788.73002
[4] Brenner, Math Comp 73 pp 1067– (2004)
[5] Hansbo, Comput Methods Appl Mech Engrg 191 pp 1895– (2002)
[6] Crouzeix, RAIRO Sér. Rouge 7 pp 33– (1973)
[7] , Galerkin finite element methods for parabolic problems, Springer-Verlag, 1997. · Zbl 0884.65097
[8] and , Finite element methods for Navier-Stokes equations: theory and algorithms, Springer-Verlag, 1986. · Zbl 0585.65077
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