Two-grid methods for nonlinear time fractional diffusion equations by [formula omitted]-Galerkin FEM

Abstract

In this paper, two efficient two-grid algorithms with L1 scheme are presented for solving two-dimensional nonlinear time fractional diffusion equations. The classical L1 scheme is considered in the time direction, and the two-grid FE method is used to approximate spatial direction. To linearize the discrete equations, the Newton iteration approach and correction technique are applied. The two-grid algorithms reduce the solution of the nonlinear fractional problem on a fine grid to one linear equation on the same fine grid and an original nonlinear problem on a much coarser grid. As a result, our algorithms save total computational cost. Theoretical analysis shows that the two-grid algorithms maintain asymptotically optimal accuracy. Moreover, the numerical experiment presented further confirms the theoretical results.