Fast calculation based on a spatial two-grid finite element algorithm for a nonlinear space-time fractional diffusion model

In this article, a spatial two-grid finite element (TGFE) algorithm is used to solve a two-dimensional nonlinear space-time fractional diffusion model and improve the computational efficiency. First, the second-order backward difference scheme is used to formulate the time approximation, where the time-fractional derivative is approximated by the weighted and shifted Grunwald difference operator. In order to reduce the computation time of the standard FE method, a TGFE algorithm is developed. The specific algorithm is to iteratively solve a nonlinear system on the coarse grid and then to solve a linear system on the fine grid. We prove the scheme stability of the TGFE algorithm and derive a priori error estimate with the convergence resultO(Delta t(2) + h(r + 1 - eta) + H2r + 2 - 2 eta). Finally, through a two-dimensional numerical calculation, we improve the computational efficiency and reduce the computation time by the TGFE algorithm.