@Article{JCM-36-492,
author = {Li , Xiaoli and Rui , Hongxing},
title = {Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media},
journal = {Journal of Computational Mathematics},
year = {2018},
volume = {36},
number = {4},
pages = {492--516},
abstract = {<p style="text-align: justify;">In this article, two block-centered finite difference schemes are introduced and analyzed
to solve the parabolic integro-differential equation arising in modeling non-Fickian flow in
porous media. One scheme is Euler backward scheme with first order accuracy in time
increment while the other is Crank-Nicolson scheme with second order accuracy in time
increment. Stability analysis and second-order error estimates in spatial mesh size for both
pressure and velocity in discrete L<sup>2&nbsp;</sup>norms are established on non-uniform rectangular grid.
Numerical experiments using the schemes show that the convergence rates are in agreement
with the theoretical analysis.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1701-m2016-0628},
url = {http://global-sci.org/intro/article_detail/jcm/12302.html}
}