Finite difference/spectral element method for one and two-dimensional Riesz space fractional advection–dispersion equations

Marziyeh Saffarian and Akbar Mohebbi

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 193, issue C, 348-370

Abstract: In this paper, we propose an efficient numerical method for the solution of one and two dimensional Riesz space fractional advection–dispersion equation. To this end, we use the Crank–Nicolson scheme to discretize this equation in temporal direction and prove that the semi-discrete scheme is unconditionally stable. Then, we apply the spectral element method in spatial directions and obtain the fully discrete scheme. We present an error estimate for the fully discrete scheme. The presented numerical results demonstrate the accuracy and efficiency of the proposed method in comparison with other schemes in literature.

Keywords: Spectral element method; Stability; Error estimate; Advection dispersion equation; Riesz space fractional derivative (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:193:y:2022:i:c:p:348-370

DOI: 10.1016/j.matcom.2021.10.020

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