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Two-Grid Method for Miscible Displacement Problem by Mixed Finite Element Methods and Mixed Finite Element Method of Characteristics

Part of: Equations and systems of special type Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  17 May 2016

Yanping Chen  and
Hanzhang Hu
Yanping Chen*
Affiliation:
School of Mathematical Science, South China Normal University, Guangzhou 520631, Guangdong, P.R. China
Hanzhang Hu*
Affiliation:
School of Mathematical Science, South China Normal University, Guangzhou 520631, Guangdong, P.R. China School of Mathematics, Jiaying University, Meizhou 514015, Guangdong, P.R. China
*
*Corresponding author. Email addresses:[email protected](Y. Chen), [email protected](H. Hu)
*Corresponding author. Email addresses:[email protected](Y. Chen), [email protected](H. Hu)
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Abstract

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is elliptic form equation for the pressure and the other is parabolic form equation for the concentration of one of the fluids. Since only the velocity and not the pressure appears explicitly in the concentration equation, we use a mixed finite element method for the approximation of the pressure equation and mixed finite element method with characteristics for the concentration equation. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method for this full discrete scheme problems. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = H2 in this paper. Finally, numerical experiment indicates that two-grid algorithm is very effective.

Keywords

Two-grid methodmiscible displacement problemmixed finite elementcharacteristic finite element method

MSC classification

Secondary: 35M13: Initial-boundary value problems for equations of mixed type 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Communications in Computational Physics , Volume 19 , Issue 5 , May 2016 , pp. 1503 - 1528
Copyright
Copyright © Global-Science Press 2016 

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