Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations

Advances in Difference Equations

article

Zhao, Jie¹  Fang, Zhichao¹  Li, Hong¹  Liu, Yang¹ 

[1] School of Mathematical Sciences, Inner Mongolia University;School of Statistics and Mathematics, Inner Mongolia University of Finance and Economics

关键词: WSGD formula;    Finite volume element method;    Nonlinear fractional mobile/immobile transport equations;    Existence and uniqueness;    Unconditional stability;    Optimal a priori error estimate;   

DOI  :  10.1186/s13662-020-02786-8

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this article, a finite volume element method with the second-order weighted and shifted Grünwald difference (WSGD) formula is proposed and studied for nonlinear time fractional mobile/immobile transport equations on triangular grids. By using the WSGD formula of approximating the Riemann–Liouville fractional derivative and an interpolation operator$I_{h}^{*}$ , a second-order fully discrete finite volume element (FVE) scheme is formulated. The existence, uniqueness, and unconditional stability for the fully discrete FVE scheme are derived, the optimal a priori error estimates in$L^{\infty }(L^{2}(\varOmega))$ and$L^{2}(H^{1}(\varOmega))$ norms are obtained, in which the convergence orders are independent of the fractional parameters. At the end of this article, two numerical examples with different nonlinear terms are given to verify the feasibility and effectiveness.

【 授权许可】

CC BY