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In this paper, the time fractional reaction-diffusion equations with theCaputo fractional derivative are solved by using the classical $L1$-formula andthe finite volume element (FVE) methods on triangular grids. The existence anduniqueness for the fully discrete FVE scheme are given. The stability resultand 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 toverify the feasibility and effectiveness.

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