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A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media
Author(s) -
Yang Danping
Publication year - 2001
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.3
Subject(s) - mathematics , mathematical analysis , compressibility , partial differential equation , finite element method , porous medium , displacement (psychology) , positive definite matrix , mixed finite element method , nonlinear system , galerkin method , porosity , thermodynamics , chemistry , physics , eigenvalues and eigenvectors , psychology , quantum mechanics , psychotherapist , organic chemistry
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