Error analysis of an ADI scheme for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions

Abstract

In this work, we consider a numerical approximation for the two-dimensional fractal mobile/immobile transport equation with weakly singular solutions, where the time first-order derivative is discretized by the backward Euler method, and the Caputo fractional derivative is approximated by the L1 scheme on a uniform mesh. The fully discrete ADI scheme is established by adding a high-order term. The stability and the convergence analyses of the fully discrete ADI scheme are analyzed in $L^2$-norm and $H^1$-norm. The numerical results show that the error estimates are sharp.