Time-stepping error bounds for fractional diffusion problems with non-smooth initial data

William McLean; Kassem Mustapha

doi:10.1016/j.jcp.2014.08.050

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arXiv · 1405.2140

Time-stepping error bounds for fractional diffusion problems with non-smooth initial data

William McLean·Kassem Mustapha

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Abstract

We apply the piecewise constant, discontinuous Galerkin method to discretize a fractional diffusion equation with respect to time. Using Laplace transform techniques, we show that the method is first order accurate at the \$n\$th time level \$t_n\$, but the error bound includes a factor \$t_n^{-1}\$ if we assume no smoothness of the initial data. We also show that for smoother initial data the growth in the error bound as \$t_n\$ decreases is milder, and in some cases absent altogether. Our error bounds generalize known results for the classical heat equation and are illustrated for a model problem.

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BibTeX RIS

William McLean, Kassem Mustapha. 2014-05-09. Time-stepping error bounds for fractional diffusion problems with non-smooth initial data. https://doi.org/10.1016/j.jcp.2014.08.050

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