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Analysis of a discontinuous finite element method for the coupled Stokes and Darcy problems. (English) Zbl 1065.76143
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.
76M10Finite element methods (fluid mechanics)
76D07Stokes and related (Oseen, etc.) flows
76S05Flows in porous media; filtration; seepage
65N15Error bounds (BVP of PDE)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
[2] · Zbl 0482.65060 · doi:10.1137/0719052
[3] · doi:10.1017/S0022112067001375
[4]Bernardi, C., Hecht, F., and Pironneau, O. (2002). Coupling Darcy and Stokes Equations for Porous Media with Cracks, Technical Report R02042, Paris VI.
[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.
[6] · doi:10.1090/S0025-5718-1989-0958870-8
[8] · Zbl 1023.76048 · doi:10.1016/S0168-9274(02)00125-3
[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.
[11] · Zbl 0514.73068 · doi:10.1002/nme.1620190405
[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.
[14] · Zbl 0969.76088 · doi:10.1137/S003613999833678X
[15] · Zbl 1037.76014 · doi:10.1137/S0036142901392766
[16] · Zbl 1037.65120 · doi:10.1137/S0036142901383910
[17] · Zbl 0906.35067 · doi:10.1016/S0021-7824(98)80102-5
[18] · Zbl 0951.65108 · doi:10.1023/A:1011591328604
[19] · Zbl 1010.65045 · doi:10.1137/S003614290037174X
[20]Rivière, B., and Yotov, I. (2003). Locally conservative coupling of Stokes and Darcy flow. SIAM J. Numer. Anal. accepted, 2004.
[22] · Zbl 0384.65058 · doi:10.1137/0715010