The finite volume element method for the two-dimensional space-fractional convection–diffusion equation

Advances in Difference Equations

Ziwen Jiang¹  Yanan Bi¹ 

[1] School of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, China;

关键词: Fractional derivative;    Finite volume element method;    Stability;    Convergence;    Convection–diffusion equation;   

DOI  :  10.1186/s13662-021-03524-4

来源: Springer

【 摘 要 】

We develop a fully discrete finite volume element scheme of the two-dimensional space-fractional convection–diffusion equation using the finite volume element method to discretize the space-fractional derivative and Crank–Nicholson scheme for time discretization. We also analyze and prove the stability and convergence of the given scheme. Finally, we validate our theoretical analysis by data from three examples.

【 授权许可】

CC BY