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Numerical approximations for a miscible displacement process in porous media. (English) Zbl 0608.76084

A reservoir simulation problem describing a miscible displacement process is stated and analyzed using Galerkin method with mesh refinement. Mathematical behavior of fluid concentrations near wells i.e. singular points is described and order of convergence analysis is performed for mesh refinement in these points. It is shown that such a numerical approximation will converge as the overall grid spacing is reduced, with an optimal O(h) rate where h denotes a typical triangle size.
Reviewer: M.M.Aral

MSC:

76S05 Flows in porous media; filtration; seepage
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76M99 Basic methods in fluid mechanics
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