Stability and pointwise-in-time convergence analysis of a finite difference scheme for a 2D nonlinear multi-term subdiffusion equation

In this paper, we aim to study the stability and convergence of a finite difference scheme for solving the two-dimensional nonlinear multi-term time fractional subdiffusion equation with weakly singular solutions. We apply the L1 scheme to discretize the multi-term temporal Caputo derivatives, a standard central difference method in space, and a backward formula to approximate the nonlinear term on the uniform mesh, respectively. Stability and pointwise-in-time error estimates are obtained for the fully discrete scheme. The global convergence order is $ \alpha_1 $, and the local convergence order is 1 in the temporal direction. The theoretical analysis is verified by some numerical results.