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

Jingjun Zhao, Wenjiao Zhao and Yang Xu

Applied Mathematics and Computation, 2023, vol. 442, issue C

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.

Keywords: Space-time fractional advection-dispersion; Hybridizable discontinuous Galerkin method; Stability; Convergence (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s009630032200813x

DOI: 10.1016/j.amc.2022.127745

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