文章基本信息

标题：Finite volume element method with the WSGD formula for nonlinear fractional mobile/immobile transport equations
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作者：Jie Zhao ; Zhichao Fang ; Hong Li 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-20
DOI：10.1186/s13662-020-02786-8
出版社：Hindawi Publishing Corporation
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 $L^{\infty }(L^,(\varOmega))$ and $L^,(H^)(\varOmega))$ 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.
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;