标题：BLOCK-CENTERED FINITE DIFFERENCE METHODS FOR NON-FICKIAN FLOW IN POROUS MEDIA
作者：Li, Xiaoli; Rui, Hongxing
作者机构：[Li, Xiaoli; Rui, Hongxing] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
通讯作者地址：[Li, XL]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：JOURNAL OF COMPUTATIONAL MATHEMATICS
关键词：Block-centered finite difference; Parabolic integro-differential; equation; Non- uniform; Error estimates; Numerical analysis
摘要：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 meshsize for both pressure and velocity in discrete L-2 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.