A Mixed Finite Volume Element Method for Time-Fractional Reaction-Diffusion Equations on Triangular Grids

Jie Zhao, Hong Li, Zhichao Fang and Yang Liu
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Jie Zhao: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Hong Li: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Zhichao Fang: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China
Yang Liu: School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, China

Mathematics, 2019, vol. 7, issue 7, 1-18

Abstract: In this article, the time-fractional reaction-diffusion equations are solved by using a mixed finite volume element (MFVE) method and the L 1 -formula of approximating the Caputo fractional derivative. The existence, uniqueness and unconditional stability analysis for the fully discrete MFVE scheme are given. A priori error estimates for the scalar unknown variable (in L 2 ( Ω ) -norm) and the vector-valued auxiliary variable (in ( L 2 ( Ω ) ) 2 -norm and H ( div , Ω ) -norm) are derived. Finally, two numerical examples in one-dimensional and two-dimensional spatial regions are given to examine the feasibility and effectiveness.

Keywords: mixed finite volume element method; time-fractional reaction-diffusion equation; existence and uniqueness analysis; unconditional stability analysis; a priori error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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