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The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows

Published online by Cambridge University Press:  03 June 2015

Buyang Li ,
Jilu Wang  and
Weiwei Sun
Buyang Li*
Affiliation:
Department of Mathematics, Nanjing University, Nanjing, P.R. China
Jilu Wang*
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
Weiwei Sun*
Affiliation:
Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
*
Email:buyangli@nju.edu.cn
Email:jiluwang2-c@my.cityu.edu.hk
Corresponding author.Email:maweiw@math.cityu.edu.hk
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Abstract

The paper is concerned with the unconditional stability and error estimates of fully discrete Galerkin-Galerkin FEMs for the equations of incompressible miscible flows in porous media. We prove that the optimal L2 error estimates hold without any time-step (convergence) conditions, while all previous works require certain time-step restrictions. Theoretical analysis is based on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of the corresponding time-discrete PDEs, which was proposed in our previous work [26, 27]. Numerical results for both two and three-dimensional flow models are presented to confirm our theoretical analysis.

Keywords

65N1265N3035K61Unconditional stabilityoptimal error estimateGalerkin FEMsincompressible miscible flows
Type
Research Article
Information
Communications in Computational Physics , Volume 15 , Issue 4 , April 2014 , pp. 1141 - 1158
Copyright
Copyright © Global Science Press Limited 2014

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