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Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations. (English) Zbl 1457.76161

Summary: Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the \(L^{2}\) norm.

MSC:

76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
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References:

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