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Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations
Author(s) -
Girault Vivette,
Li Jizhou,
Rivière Beatrice M.
Publication year - 2017
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.22092
Subject(s) - mathematics , sobolev space , discontinuous galerkin method , convergence (economics) , mathematical analysis , weak formulation , finite element method , norm (philosophy) , partial differential equation , galerkin method , nonlinear system , weak solution , balanced flow , porous medium , displacement (psychology) , partial derivative , porosity , boundary value problem , physics , economics , psychotherapist , thermodynamics , economic growth , psychology , geotechnical engineering , engineering , quantum mechanics , political science , law
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. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017