Analysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth Data

This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem with nonsmooth data, and then prove that the time-steeping scheme possesses optimal convergence rates in $ L^2(0,T;L^2(\Omega)) $-norm and $ L^2(0,T;H_0^1(\Omega)) $-norm with respect to the regularity of the solution. Finally, numerical results are provided to verify the theoretical results.

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