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

Zhichao Fang
2021 arXiv   pre-print
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 a priori error estimate in L^2(Ω)-norm are derived, but it is difficult to obtain the corresponding results in H^1(Ω)-norm, so another analysis technique is introduced and used to
more » ... chieve our goal. Finally, two numerical examples in different spatial dimensions are given to verify the feasibility and effectiveness.
arXiv:2101.12541v1 fatcat:lxxijgauongohku3qhojvliho4