Year: 2018
Author: Xiaoli Li, Hongxing Rui
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 492–516
Abstract
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 L2 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1701-m2016-0628
Journal of Computational Mathematics, Vol. 36 (2018), Iss. 4 : pp. 492–516
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Block-centered finite difference Parabolic integro-differential equation Non-uniform Error estimates Numerical analysis.