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- W4298849596 abstract "In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for such a problem due to the low regularity of its exact solution. Using a delicate energy analysis, {it a priori} optimal error bounds in $L^2(Omega)$-, $H^1(Omega)$-norms, and a quasi-optimal bound in $L^{infty}(Omega)$-norm are derived for the semidiscrete FEM for cases with smooth and nonsmooth initial data. The main tool of our analysis is based on a repeated use of an integral operator and use of a $t^m$ type of weights to take care of the singular behavior of the continuous solution at $t=0.$ The generalized Leibniz formula for fractional derivatives is found to play a key role in our analysis. Numerical experiments are presented to illustrate some of the theoretical results." @default.
- W4298849596 created "2022-10-02" @default.
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- W4298849596 date "2016-05-30" @default.
- W4298849596 modified "2023-09-23" @default.
- W4298849596 title "Optimal error analysis of a FEM for fractional diffusion problems by energy arguments" @default.
- W4298849596 doi "https://doi.org/10.48550/arxiv.1605.09104" @default.
- W4298849596 hasPublicationYear "2016" @default.
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