Analysis of a time-stepping scheme for time fractional diffusion problems with nonsmooth data
Provides theoretical convergence guarantees for numerical solutions of fractional diffusion equations with nonsmooth initial data, important for computational mathematics.
The paper proves optimal convergence rates for a time-stepping scheme applied to time fractional diffusion problems with nonsmooth data, validated by numerical experiments.
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(Ω)) $-norm and $ L^2(0,T;H_0^1(Ω)) $-norm with respect to the regularity of the solution. Finally, numerical results are provided to verify the theoretical results.