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Numerical Algorithms

, Volume 81, Issue 3, pp 879–914 | Cite as

Numerical solution of a miscible displacement problem with dispersion term using a two-grid mixed finite element approach

  • Hanzhang Hu
  • Yiping Fu
  • Jie ZhouEmail author
Original Paper
  • 56 Downloads

Abstract

A nonlinear system of two coupled partial differential equations is derived to describe miscible displacement of one incompressible fluid by another in a porous medium. A mixed finite element method (MFEM) is applied to the pressure equation, and the mixed finite element method with characteristics(CMFEM) is proposed to solve the concentration equation. A two-grid algorithm is considered to linearize nonlinear system of two coupled partial differential equations models. Moreover, the error estimates are carried out for the two-grid algorithm in this paper. Numerical experiments are presented to show the efficiency of the two-grid algorithm.

Keywords

Two-grid method Miscible displacement Mixed finite element method Characteristic mixed finite element method 

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Notes

Acknowledgments

We are grateful to the two anonymous referees for useful comments and suggestions.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsJiaying UniversityMeizhouPeople’s Republic of China
  2. 2.School of MathematicsSouth China University of TechnologyGuangzhouPeople’s Republic of China
  3. 3.School of Mathematics and Computational ScienceXiangtan UniversityXiangtanPeople’s Republic of China

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