A fast time two-mesh finite volume element algorithm for the nonlinear time-fractional coupled diffusion model

In this work, a fast second-order finite volume element (FVE) algorithm is proposed to solve the nonlinear time-fractional coupled diffusion model based on the time two-mesh (TT-M) computing method. In this algorithm, the integer and RiemannLiouville fractional derivatives are approximated by the second-order backward difference formula and the WSGD formula respectively, the time interval is divided into coarse and fine meshes, then the three steps TT-M FVE algorithm is constructed by using the interpolation operator. The existence and uniqueness for the TT-M FVE algorithm are analyzed in detail, the asymptotically optimal a priori error estimates for variables u and v in the discrete L-infinity(L-2(Omega)) and L-2(H-1(Omega) norms are obtained. It is shown that when time coarse and fine mesh sizes satisfy tau(c) = O(tau(1/2)(f)), the fast algorithm can achieve the same accuracy as the FVE algorithm, and reduce more computational cost. Finally, some numerical results are given to demonstrate the efficiency of the proposed algorithm.