Block-Centered Finite Difference Methods for Non-Fickian Flow in Porous Media (Journal of Computational Mathematics, 2018)
In this article, two block-centered finite difference schemes are introduced and analyzedto solve the parabolic integro-differential equation arising in modeling non-Fickian flow inporous media. One scheme is Euler backward scheme with first order accuracy in timeincrement while the other is Crank-Nicolson scheme with second order accuracy in timeincrement. Stability analysis and second-order error estimates in spatial mesh size for bothpressure 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 agreementwith the theoretical analysis.