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Analysis of a time-stepping scheme for time fractional diffusion problems with nonsmooth data

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arxiv 1804.10552 v1 pith:GK55JB5H submitted 2018-04-27 math.NA cs.NA

Binjie Li , Hao Luo , Xiaoping Xie This is my paper · ORCID
classification math.NAcs.NA
keywords datanonsmoothschemeconvergencediffusionfractionalnormomega
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abstract

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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  1. Analysis of the L1 scheme for fractional wave equations with nonsmooth data

    math.NA 2019-08 conditional novelty 7.0 of 10

    The standard L1 scheme is shown to be O(tau^(3-alpha)) accurate in the L2 norm for fractional wave equations with nonsmooth data, and a modified version reaches O(tau^2).

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