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Numerical analysis of finite element methods for miscible displacements in porous media
Author(s) -
Malta Sandra M. C.,
Loula Abimael F. D.
Publication year - 1998
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/(sici)1098-2426(199807)14:4<519::aid-num5>3.0.co;2-n
Subject(s) - finite element method , mathematics , partial differential equation , discretization , porous medium , displacement (psychology) , convergence (economics) , nonlinear system , method of mean weighted residuals , galerkin method , darcy's law , mixed finite element method , compressibility , mathematical analysis , partial derivative , mechanics , porosity , materials science , structural engineering , physics , engineering , quantum mechanics , economics , composite material , psychotherapist , economic growth , psychology
Finite element methods are used to solve a coupled system of nonlinear partial differential equations, which models incompressible miscible displacement in porous media. Through a backward finite difference discretization in time, we define a sequentially implicit time‐stepping algorithm that uncouples the system at each time‐step. The Galerkin method is employed to approximate the pressure, and accurate velocity approximations are calculated via a post‐processing technique involving the conservation of mass and Darcy's law. A stabilized finite element ( SUPG ) method is applied to the convection–diffusion equation delivering stable and accurate solutions. Error estimates with quasi‐optimal rates of convergence are derived under suitable regularity hypotheses. Numerical results are presented confirming the predicted rates of convergence for the post‐processing technique and illustrating the performance of the proposed methodology when applied to miscible displacements with adverse mobility ratios. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 519–548, 1998