@Article{CiCP-15-4,
author = {},
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 = {<p style="text-align: justify;">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<sup>2&nbsp;</sup>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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.080313.051213s},
url = {https://global-sci.com/article/80526/the-stability-and-convergence-of-fully-discrete-galerkin-galerkin-fems-for-porous-medium-flows}
}