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Analysis of a combined mixed finite element and discontinuous Galerkin method for incompressible two‐phase flow in porous media
Author(s) -
Kou Jisheng,
Sun Shuyu
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2854
Subject(s) - mathematics , uniqueness , compressibility , finite element method , porous medium , discontinuous galerkin method , galerkin method , saturation (graph theory) , mathematical analysis , constructive , mixed finite element method , incompressible flow , flow (mathematics) , porosity , mechanics , geometry , thermodynamics , materials science , physics , composite material , process (computing) , combinatorics , computer science , operating system
We analyze a combined method consisting of the mixed finite element method for pressure equation and the discontinuous Galerkin method for saturation equation for the coupled system of incompressible two‐phase flow in porous media. The existence and uniqueness of numerical solutions are established under proper conditions by using a constructive approach. Optimal error estimates in L 2 ( H 1 ) for saturation and in L ∞ ( H (div)) for velocity are derived. Copyright © 2013 John Wiley & Sons, Ltd.