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Volume 15, Issue 4
The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows

Buyang Li, Jilu Wang & Weiwei Sun

DOI: 10.4208/cicp.080313.051213s

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

Published online: 2014-04

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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.

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@Article{CiCP-15-1141, author = {Buyang Li, Jilu Wang and Weiwei Sun}, title = {The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows}, journal = {Communications in Computational Physics}, year = {2014}, volume = {15}, number = {4}, pages = {1141--1158}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.080313.051213s}, url = {http://global-sci.org/intro/article_detail/cicp/7131.html} }
TY - JOUR T1 - The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows AU - Buyang Li, Jilu Wang & Weiwei Sun JO - Communications in Computational Physics VL - 4 SP - 1141 EP - 1158 PY - 2014 DA - 2014/04 SN - 15 DO - http://doi.org/10.4208/cicp.080313.051213s UR - https://global-sci.org/intro/article_detail/cicp/7131.html KW - AB -

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.

Buyang Li, Jilu Wang and Weiwei Sun. (2014). The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows. Communications in Computational Physics. 15 (4). 1141-1158. doi:10.4208/cicp.080313.051213s
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