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arXiv · 1905.05732

Optimal order finite element approximations for variable-order time-fractional diffusion equations

Xiangcheng Zheng·Fanhai Zeng·Hong Wang
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Abstract

We study a fully discrete finite element method for variable-order time-fractional diffusion equations with a time-dependent variable order. Optimal convergence estimates are proved with the first-order accuracy in time (and second order accuracy in space) under the uniform or graded temporal mesh without full regularity assumptions of the solutions. Numerical experiments are presented to substantiate the analysis.

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Xiangcheng Zheng, Fanhai Zeng, Hong Wang. 2019-05-14. Optimal order finite element approximations for variable-order time-fractional diffusion equations. https://arxiv.org/abs/1905.05732

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