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arXiv · 2101.12541

Finite Volume Element Methods for Two-Dimensional Time Fractional Reaction-Diffusion Equations on Triangular Grids

Zhichao Fang·Jie Zhao·Hong Li·Yang Liu
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Abstract

In this paper, the time fractional reaction-diffusion equations with the Caputo fractional derivative are solved by using the classical $L1$-formula and the finite volume element (FVE) methods on triangular grids. The existence and uniqueness for the fully discrete FVE scheme are given. The stability result and optimal \textit{a priori} error estimate in $L^2(\Omega)$-norm are derived, but it is difficult to obtain the corresponding results in $H^1(\Omega)$-norm, so another analysis technique is introduced and used to achieve our goal. Finally, two numerical examples in different spatial dimensions are given to verify the feasibility and effectiveness.

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Zhichao Fang, Jie Zhao, Hong Li, Yang Liu. 2021-01-29. Finite Volume Element Methods for Two-Dimensional Time Fractional Reaction-Diffusion Equations on Triangular Grids. https://arxiv.org/abs/2101.12541

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