Rivière, Béatrice; Yotov, Ivan Locally conservative coupling of Stokes and Darcy flows. (English) Zbl 1084.35063 SIAM J. Numer. Anal. 42, No. 5, 1959-1977 (2005). Summary: A locally conservative numerical method for solving the coupled Stokes and Darcy flows problem is formulated and analyzed. The approach employs the mixed finite element method for the Darcy region and the discontinuous Galerkin method for the Stokes region. A discrete inf-sup condition and optimal error estimates are derived. Cited in 137 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 76D07 Stokes and related (Oseen, etc.) flows 76S05 Flows in porous media; filtration; seepage 76M10 Finite element methods applied to problems in fluid mechanics Keywords:porous media flow; incompressible fluid flow; discontinuous Galerkin; mixed finite element; error estimates; inf-sup condition PDF BibTeX XML Cite \textit{B. Rivière} and \textit{I. Yotov}, SIAM J. Numer. Anal. 42, No. 5, 1959--1977 (2005; Zbl 1084.35063) Full Text: DOI OpenURL