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In this paper, time fractional reaction–diffusion equations with the Caputo fractional derivative are solved by using the classical-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 results and optimal  a priori  error estimate in-norm are derived, but it is difficult to obtain the corresponding results in-norm, so another analysis technique is introduced and used to achieve our goal. Finally, some numerical results are given to verify the feasibility and effectiveness.

Finite volume element methods for two-dimensional time fractional reaction–diffusion equations on triangular grids