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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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Τίτλος: The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.
Συγγραφείς: 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
Πηγή: Applied Numerical Mathematics. Oct2026, Vol. 228, p57-70. 14p.
Θεματικοί όροι: *Galerkin methods, *Transport equation, *Numerical analysis, *Transport theory, *Numerical calculations
Περίληψη: 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]
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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>
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  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]
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        Value: 10.1016/j.apnum.2026.05.009
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      – Code: eng
        Text: English
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        PageCount: 14
        StartPage: 57
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      – SubjectFull: Galerkin methods
        Type: general
      – SubjectFull: Transport equation
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      – SubjectFull: Numerical analysis
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      – TitleFull: The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.
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              M: 10
              Text: Oct2026
              Type: published
              Y: 2026
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