Fast two-grid finite volume element algorithms combined with Crank-Nicolson scheme for the nonlinear time fractional mobile/immobile transport model

In this article, fast time second-order two-grid algorithms are proposed for solving the nonlinear mobile/immobile transport model with the Riemann-Liouville time fractional derivative by using the finite volume element algorithm and the Crank-Nicolson scheme. The fast algorithms involve solving the nonlinear system on the spatial coarse grid (with grid size H) and then solving the linearized system on spatial fine grid (with grid size h). The stability results for the two-grid Crank-Nicolson finite volume element (CNFVE) algorithms are given, and the optimal error estimates in the discrete L∞(L2(Ω)) and L2(H1(Ω)) norms are obtained. It is shown that the fast two-grid CNFVE algorithms can achieve asymptotically optimal approximation, as long as the spatial coarse and fine grid sizes satisfy H=O(h1/2) (in the discrete L∞(L2(Ω)) norm) and H=O(h1/4) (in the discrete L2(H1(Ω)) norm). The numerical results are given to validate that the proposed fast algorithms are very effective.