An optimal error estimate for the two-dimensional nonlinear time fractional advection-diffusion equation with smooth and non-smooth solutions

摘要

In this paper, a linearized L1 Legendre-Galerkin spectral method for the two-dimensional nonlinear time fractional advection-diffusion equation is derived. The numerical method is stable without the CFL conditions based on the error splitting argument technique and the discrete fractional Gronwall type inequality. We also consider the case of non-smooth solutions by adding some correction terms. The numerical experiments are given to verify the theoretical analysis and the effectiveness of the correction method. (C) 2019 Elsevier Ltd. All rights reserved.