标题：A high-order fully conservative block-centered finite difference method for the time-fractional advection-dispersion equation
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：[Rui, HX]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：APPLIED NUMERICAL MATHEMATICS
关键词：High-order; Block-centered finite difference; Time-fractional; advection-dispersion equation; Priori estimates; Numerical experiments
摘要：Based on the weighted and shifted Grunwald-Letnikov difference operator, a new high order block-centered finite difference method is derived for the time-fractional advection-dispersion equation by introducing an auxiliary flux variable to guarantee full mass conservation. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O(Delta t(3) + h(2) + k(2)) both for solute concentration and the auxiliary flux variable are established on non-uniform rectangular grids, where Delta t, h and k are the step sizes in time, space in x-and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis. (C) 2017 IMACS. Published by Elsevier B.V. All rights reserved.