Finite element method for two-dimensional space-fractional advection–dispersion equations

Yanmin Zhao, Weiping Bu, Jianfei Huang, Da-Yan Liu and Yifa Tang

Applied Mathematics and Computation, 2015, vol. 257, issue C, 553-565

Abstract: The backward Euler and Crank–Nicolson–Galerkin fully-discrete approximate schemes for two-dimensional space-fractional advection–dispersion equations are established. Firstly, we prove that the corresponding variational problem has a unique solution, and the proposed fully-discrete schemes are unconditionally stable, whose solutions are all unique. Secondly, the optimal error estimates are derived by use of properties of projection operator and fractional derivatives. Finally, numerical examples demonstrate effectiveness of numerical schemes and confirm the theoretical analysis.

Keywords: Space-fractional advection–dispersion equation; Backward Euler scheme; Crank–Nicolson–Galerkin scheme; Finite element method; Optimal error estimate (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations: View citations in EconPapers (13)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:257:y:2015:i:c:p:553-565

DOI: 10.1016/j.amc.2015.01.016

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