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Networks and Heterogeneous Media

2026, Volume 21, Issue 2: 387-401. doi: 10.3934/nhm.2026018
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A novel numerical method on a posteriori mesh for a singularly perturbed convection-diffusion problem with mixed type boundary conditions

  • 1.
    Institute of Mathematics, Zhejiang Wanli University, Ningbo 315100, P.R. China
  • 2.
    School of Data Science, Zhuhai College of Science and Technology, Zhuhai 519041, China
  • Published: 24 March 2026

  • This article introduces a novel numerical method for solving a singularly-perturbed convection-diffusion problem with mixed type boundary conditions. The approach begins by transforming the second-order boundary value problem into a system of first-order differential equations. The stability result of its corresponding differential operator vector is obtained although the system of equations is in a special form. The transformed system is approximated through a hybrid difference method, followed by a posteriori error analysis that relies on the stability result of the differential operator vector. A posteriori mesh and approximation solution are derived by designing a solution-adaptive algorithm derived from the a posteriori error bound. Finally, the second-order uniform convergence of the novel numerical method is corroborated by numerical experiments.

    Citation: Jian Huang, Zhongdi Cen, Xianbin Wu. A novel numerical method on a posteriori mesh for a singularly perturbed convection-diffusion problem with mixed type boundary conditions[J]. Networks and Heterogeneous Media, 2026, 21(2): 387-401. doi: 10.3934/nhm.2026018

    Related Papers:

  • This article introduces a novel numerical method for solving a singularly-perturbed convection-diffusion problem with mixed type boundary conditions. The approach begins by transforming the second-order boundary value problem into a system of first-order differential equations. The stability result of its corresponding differential operator vector is obtained although the system of equations is in a special form. The transformed system is approximated through a hybrid difference method, followed by a posteriori error analysis that relies on the stability result of the differential operator vector. A posteriori mesh and approximation solution are derived by designing a solution-adaptive algorithm derived from the a posteriori error bound. Finally, the second-order uniform convergence of the novel numerical method is corroborated by numerical experiments.



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