Burman, Erik; Hansbo, Peter Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. (English) Zbl 1077.76037 Numer. Methods Partial Differ. Equations 21, No. 5, 986-997 (2005). 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. Cited in 1 ReviewCited in 59 Documents 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 Keywords:discontinuous Galerkin method; Convergence; vanishing viscosity PDFBibTeX XMLCite \textit{E. Burman} and \textit{P. Hansbo}, Numer. Methods Partial Differ. Equations 21, No. 5, 986--997 (2005; Zbl 1077.76037) Full Text: DOI Link 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 · doi:10.1007/978-1-4612-3172-1 [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 · doi:10.1007/978-3-662-03359-3 [8] and , Finite element methods for Navier-Stokes equations: theory and algorithms, Springer-Verlag, 1986. · Zbl 0585.65077 · doi:10.1007/978-3-642-61623-5 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.