H1-norm error analysis of a robust ADI method on gradedmesh for three-dimensional subdiffusion problems

This work proposes a robust ADI scheme on graded mesh for solving three-dimensional subdiffusion problems. The Caputo fractional derivative is discretized by L1 scheme, where the graded mesh is used to eliminate the weak singular behavior of the exact solution at the initial time t=0. The spatial derivatives are approximated by the finite difference method. Based on the improved discrete fractional Gronwall inequality, we prove the stability and alpha-robust H-1-norm convergence, in which the error bound does not blow up when the order of fractional derivative alpha -> 1(-).The3D numerical examples are proposed to verify the efficiency and accuracy of the ADI method. The CPU time is also provided, which shows the proposed method is very efficient for 3D subdiffusion problems.