Numerical Methods for Partial Differential Equations · 2001 · 60 citations · 10 references
Numerical AnalysisEngineeringFluid MechanicsPorous Medium EquationsComputational MechanicsPorous MediumPorous BodyCompressible FlowFluid PropertiesPorous MediaBoundary Element MethodIncompressible FlowNonlinear Parabolic SystemMultiphase FlowNumerical Method For Partial Differential EquationFinite Element MethodPore StructurePorothermoelasticityMiscible Displacement
Abstract A miscible displacement of one compressible fluid by another in a porous medium is governed by a nonlinear parabolic system. A new mixed finite element method, in which the mixed element system is symmetric positive definite and the flux equation is separated from pressure equation, is introduced to solve the pressure equation of parabolic type, and a standard Galerkin method is used to treat the convection‐diffusion equation of concentration of one of the fluids. The convergence of the approximate solution with an optimal accuracy in L 2 ‐norm is proved. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 229–249, 2001
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