Commun. Comput. Phys., 15 (2014), pp. 1141-1158.


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

Buyang Li 1, Jilu Wang 2, Weiwei Sun 2*

1 Department of Mathematics, Nanjing University, Nanjing, P.R. China.
2 Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong.

Received 8 March 2013; Accepted (in revised version) 5 December 2013
Available online 21 January 2014
doi:10.4208/cicp.080313.051213s

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 L^2 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.

AMS subject classifications: 65N12, 65N30, 35K61

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Key words: Unconditional stability, optimal error estimate, Galerkin FEMs, incompressible miscible flows.

*Corresponding author.
Email: buyangli@nju.edu.cn (B. Li), jiluwang2-c@my.cityu.edu.hk (J. Wang), maweiw@math.cityu.edu.hk (W. Sun)
 

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