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Abstract <p>In this paper, a high-order local discontinuous Galerkin (LDG) method is proposed to solve the variable-order (VO) fractional mobile-immobile advection-dispersion equation with the Coimbra VO fractional derivative operator. The LDG method in space and the finite difference method in time are the foundations for the method proposed in this paper. We demonstrate that the scheme is unconditionally stable and convergent for <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11470_2025_2179_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="87" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha (t) \in (0,1)\)</EquationSource> <!--ComMat2470203Yang-m1--> </InlineEquation>. Finally, the correctness of the theoretical analysis is verified by some numerical experiments.</p>

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Local Discontinuous Galerkin Method for the Variable-Order Fractional Mobile-Immobile Advection-Dispersion Equation

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • Miaomiao Yang,
  • Lijie Liu,
  • Leilei Wei

摘要

Abstract

In this paper, a high-order local discontinuous Galerkin (LDG) method is proposed to solve the variable-order (VO) fractional mobile-immobile advection-dispersion equation with the Coimbra VO fractional derivative operator. The LDG method in space and the finite difference method in time are the foundations for the method proposed in this paper. We demonstrate that the scheme is unconditionally stable and convergent for \(\alpha (t) \in (0,1)\) . Finally, the correctness of the theoretical analysis is verified by some numerical experiments.