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A combined hybrid mixed element method for incompressible miscible displacement problem with local discontinuous Galerkin procedure
Author(s) -
Zhang Jiansong,
Han Huiran,
Guo Hui,
Shen Xiaomang
Publication year - 2020
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.22495
Subject(s) - discontinuous galerkin method , mathematics , finite element method , convergence (economics) , displacement (psychology) , mixed finite element method , galerkin method , compressibility , computation , extended finite element method , mathematical analysis , pressure correction method , mathematical optimization , algorithm , mechanics , physics , psychology , economics , psychotherapist , thermodynamics , economic growth
In this article, we propose a combined hybrid discontinuous mixed finite element method for miscible displacement problem with local discontinuous Galerkin method. Here, to obtain more accurate approximation and deal with the discontinuous case, we use the hybrid mixed element method to approximate the pressure and velocity, and use the local discontinuous Galerkin finite element method for the concentration. Compared with other combined methods, this method can improve the efficiency of computation, deal with the discontinuous problem well and keep local mass balance. We study the convergence of this method and give the corresponding optimal error estimates in L ∞ ( L 2 ) for velocity and concentration and the super convergence in L ∞ ( H 1 ) for pressure. Finally, we also present some numerical examples to confirm our theoretical analysis.