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Rivière, Béatrice

Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems. (English) Zbl 1065.76143

J. Sci. Comput. 22-23, 479-500 (2005).
Summary: The coupled Stokes and Darcy flows problem is solved by the locally conservative discontinuous Galerkin method. Optimal error estimates are derived for fluid velocity and pressure.

Cited in 86 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76D07 Stokes and related (Oseen, etc.) flows
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:

subsurface flow; optimal error estimates; interface conditions
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\textit{B. Rivière}, J. Sci. Comput. 22--23, 479--500 (2005; Zbl 1065.76143)
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References:

[4] Bernardi, C., Hecht, F., and Pironneau, O. (2002). Coupling Darcy and Stokes Equations for Porous Media with Cracks, Technical Report R02042, Paris VI. · Zbl 1079.76041
[5] Brenner, S. (2003). Korn’s inequalities for piecewise H 1 vector fields Mathematics of Computation, S 0025-5718(03)01579-5, Article electronically published.
[10] Ewing, R. E., Iliev, O. P., and Lazarov, R. D. (1992). Numerical Simulation of Contamination Transport Due to Flow in Liquid and Porous Media, Technical Report 1992-10, Enhanced Oil Recovery Institute, University of Wyoming.
[12] Girault, V., Rivière, B., and Wheeler, M. F. (2002). A Discontinuous Galerkin Method With Non-Overlapping Domain Decomposition for the Stokes and Navier-Stokes Problems, Technical Report TICAM 02-08, to appear in Mathematics of Computation. · Zbl 1057.35029
[20] Rivière, B., and Yotov, I. (2003). Locally conservative coupling of Stokes and Darcy flow. SIAM J. Numer. Anal. accepted, 2004. · Zbl 1084.35063
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