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Yin, Zhe; Jiang, Ziwen; Xu, Qiang

A discontinuous finite volume method for the Darcy-Stokes equations. (English) Zbl 1264.76070

J. Appl. Math. 2012, Article ID 761242, 16 p. (2012).
Summary: We propose a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-order \(L^2\)-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

Cited in 9 Documents

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65N08 Finite volume methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
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\textit{Z. Yin} et al., J. Appl. Math. 2012, Article ID 761242, 16 p. (2012; Zbl 1264.76070)
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References:

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