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The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.

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Title: The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.
Authors: Wei, Leilei1,2 (AUTHOR) leileiwei@haut.edu.cn, Chen, Yanping1,3 (AUTHOR) ypchen@njupt.edu.cn, Qin, Fangfang3 (AUTHOR) ffqin@njupt.edu.cn, Huang, Jian4 (AUTHOR) huangjian213@xtu.edu.cn, Li, Peng5 (AUTHOR) lipeng@haut.edu.cn
Source: Applied Numerical Mathematics. Oct2026, Vol. 228, p57-70. 14p.
Subjects: Galerkin methods, Transport equation, Numerical analysis, Transport theory, Numerical calculations
Abstract: Transport equations with distributed-order memory kernels arise naturally in modeling anomalous transport and multi-scale memory effects in complex media. Such models capture a wide spectrum of relaxation behaviors and pose substantial challenges for numerical approximation, particularly in higher dimensions. In this work, we propose a fully discrete scheme for the two-dimensional transport equation with distributed-order memory kernel. The method employs a Grünwald-type approximation for the distributed-order derivative in time, combined with a discontinuous Galerkin method on triangular meshes for spatial discretization. We rigorously establish the unconditional stability and convergence of the scheme. A set of numerical experiments is presented to confirm the accuracy, robustness, and flexibility of the proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 194254088
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PubTypeId: academicJournal
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  Label: Title
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  Data: The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.
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  Data: <searchLink fieldCode="AR" term="%22Wei%2C+Leilei%22">Wei, Leilei</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> leileiwei@haut.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Chen%2C+Yanping%22">Chen, Yanping</searchLink><relatesTo>1,3</relatesTo> (AUTHOR)<i> ypchen@njupt.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Qin%2C+Fangfang%22">Qin, Fangfang</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> ffqin@njupt.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Huang%2C+Jian%22">Huang, Jian</searchLink><relatesTo>4</relatesTo> (AUTHOR)<i> huangjian213@xtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Li%2C+Peng%22">Li, Peng</searchLink><relatesTo>5</relatesTo> (AUTHOR)<i> lipeng@haut.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Applied+Numerical+Mathematics%22">Applied Numerical Mathematics</searchLink>. Oct2026, Vol. 228, p57-70. 14p.
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  Data: <searchLink fieldCode="DE" term="%22Galerkin+methods%22">Galerkin methods</searchLink><br /><searchLink fieldCode="DE" term="%22Transport+equation%22">Transport equation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Transport+theory%22">Transport theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+calculations%22">Numerical calculations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Transport equations with distributed-order memory kernels arise naturally in modeling anomalous transport and multi-scale memory effects in complex media. Such models capture a wide spectrum of relaxation behaviors and pose substantial challenges for numerical approximation, particularly in higher dimensions. In this work, we propose a fully discrete scheme for the two-dimensional transport equation with distributed-order memory kernel. The method employs a Grünwald-type approximation for the distributed-order derivative in time, combined with a discontinuous Galerkin method on triangular meshes for spatial discretization. We rigorously establish the unconditional stability and convergence of the scheme. A set of numerical experiments is presented to confirm the accuracy, robustness, and flexibility of the proposed method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Applied Numerical Mathematics is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1016/j.apnum.2026.05.009
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 57
    Subjects:
      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Transport equation
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Transport theory
        Type: general
      – SubjectFull: Numerical calculations
        Type: general
    Titles:
      – TitleFull: The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.
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            NameFull: Wei, Leilei
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            NameFull: Chen, Yanping
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            NameFull: Qin, Fangfang
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            NameFull: Huang, Jian
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            NameFull: Li, Peng
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          Dates:
            – D: 01
              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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              Value: 228
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            – TitleFull: Applied Numerical Mathematics
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