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Error estimates of finite volume element method for the pollution in groundwater flow. (English) Zbl 1157.76030

Summary: We study finite volume element methods for numerical solution of the pollution in groundwater flow in a two-dimensional convex polygonal domain. These type of flows realizes the uniform transport in fully saturated incompressible porous media, which may be anisotropic with respect to hydraulic conductivity, but features a direction independent of dispersivity. A fully finite volume scheme is analyzed. The discretization is performed via a planar mesh consisting of piecewise triangles, and optimal order error estimates in \(H^{1}\) and \(L^{2}\) norms are obtained.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
76S05 Flows in porous media; filtration; seepage
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
86A05 Hydrology, hydrography, oceanography
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References:

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