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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]
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Database: Engineering Source
Description
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]
ISSN:01689274
DOI:10.1016/j.apnum.2026.05.009