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Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations

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  • Zhao, Jingjun
  • Zhao, Wenjiao
  • Xu, Yang

Abstract

This work focuses on the numerical solution of the initial and boundary value problems for space-time fractional advection-diffusion equations. The well-posedness of the weak solutions is shown by Lax-Milgram lemma. Two fully discrete methods are established. The main idea is based on a hybridizable discontinuous Galerkin approach in spatial direction and two finite difference schemes in temporal direction: L1 formula, the weighted and shifted Grünwald-Letnikov formula. The stability and convergence analyses of the proposed methods are derived in detail. Several numerical experiments are provided to illustrate the theoretical results.

Suggested Citation

  • Zhao, Jingjun & Zhao, Wenjiao & Xu, Yang, 2023. "Hybridizable discontinuous Galerkin methods for space-time fractional advection-dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    • Handle: RePEc:eee:apmaco:v:442:y:2023:i:c:s009630032200813x
    DOI: 10.1016/j.amc.2022.127745
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    References listed on IDEAS

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    1. Zhao, Yanmin & Bu, Weiping & Huang, Jianfei & Liu, Da-Yan & Tang, Yifa, 2015. "Finite element method for two-dimensional space-fractional advection–dispersion equations," Applied Mathematics and Computation, Elsevier, vol. 257(C), pages 553-565.
    2. Karaaslan, Mehmet Fatih & Celiker, Fatih & Kurulay, Muhammet, 2016. "Approximate solution of the Bagley–Torvik equation by hybridizable discontinuous Galerkin methods," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 51-58.
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