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arXiv · 1709.09136

Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions

Natalia Kopteva
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Abstract

An initial-boundary value problem with a Caputo time derivative of fractional order $\alpha\in(0,1)$ is considered, solutions of which typically exhibit a singular behaviour at an initial time. For this problem, we give a simple framework for the analysis of the error of L1-type discretizations on graded and uniform temporal meshes in the $L_\infty$ and $L_2$ norms. This framework is employed in the analysis of both finite difference and finite element spatial discretiztions. Our theoretical findings are illustrated by numerical experiments.

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Natalia Kopteva. 2017-09-26. Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions. https://arxiv.org/abs/1709.09136

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