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Two‐grid method for miscible displacement problem with dispersion by finite element method of characteristics
Author(s) -
Chen Yanping,
Hu Hanzhang
Publication year - 2021
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900275
Subject(s) - finite element method , mixed finite element method , extended finite element method , nonlinear system , compressibility , grid , displacement (psychology) , mathematics , dispersion (optics) , porous medium , pressure correction method , incompressible flow , mathematical analysis , flow (mathematics) , mathematical optimization , mechanics , materials science , geometry , physics , porosity , engineering , structural engineering , psychology , optics , quantum mechanics , composite material , psychotherapist
A combined method consisting of the mixed finite element method for the pressure equation and finite element method with characteristics for the concentration equation is proposed to solve the coupled system of incompressible two‐phase flow in porous media. Two‐grid algorithm based on the Newton iteration method is developed and analyzed for the nonlinear coupled system. It is shown, both theoretically and numerically, that our schemes are efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfy H = O ( h 1 / 2 ) .