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

The Stability and Convergence of Fully Discrete Galerkin-Galerkin FEMs for Porous Medium Flows
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Year:    2014

Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.080313.051213s

Communications in Computational Physics, Vol. 15 (2014), Iss. 4 : pp. 1141–1158

Published online:    2014-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:   

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