A high-order fully conservative block-centered finite difference method for the time-fractional advection-dispersion equation

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.