A Crank–Nicolson Finite Volume Element Method for Time Fractional Sobolev Equations on Triangular Grids

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

Mathematics, 2020, vol. 8, issue 9, 1-17

Abstract: In this paper, a finite volume element (FVE) method is proposed for the time fractional Sobolev equations with the Caputo time fractional derivative. Based on the L 1 -formula and the Crank–Nicolson scheme, a fully discrete Crank–Nicolson FVE scheme is established by using an interpolation operator I h * . The unconditional stability result and the optimal a priori error estimate in the L 2 ( Ω ) -norm for the Crank–Nicolson FVE scheme are obtained by using the direct recursive method. Finally, some numerical results are given to verify the time and space convergence accuracy, and to examine the feasibility and effectiveness for the proposed scheme.

Keywords: finite volume element method; Crank–Nicolson scheme; L 1-formula; time fractional Sobolev equation; unconditional stability; optimal a priori error estimate (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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