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 ] School of Mathematics, Shandong University, Jinan; Shandong; 250100, China
来源：Applied Numerical Mathematics
摘要：Based on the weighted and shifted Grünwald–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(Δt3+h2+k2) both for solute concentration and the auxiliary flux variable are established on non-uniform rectangular grids, where Δt, 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.