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Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems

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  • Zhang, Jin
  • Liu, Xiaowei

Abstract

In this article, we analyze convergence of a weak Galerkin method on Bakhvalov-type mesh. This method uses piecewise polynomials of degree k≥1 on the interior and piecewise constant on the boundary of each element. To obtain uniform convergence, we carefully define the penalty parameter and a new interpolant which is based on the characteristic of the Bakhvalov-type mesh. Then the method is proved to be convergent with optimal order, which is confirmed by numerical experiments.

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  • Zhang, Jin & Liu, Xiaowei, 2022. "Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 393-403.
    • Handle: RePEc:eee:matcom:v:200:y:2022:i:c:p:393-403
    DOI: 10.1016/j.matcom.2022.04.023
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    References listed on IDEAS

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    1. Wang, Xiuli & Zhai, Qilong & Wang, Ruishu & Jari, Rabeea, 2018. "An absolutely stable weak Galerkin finite element method for the Darcy–Stokes problem," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 20-32.
    2. Zhang, Jin & Lv, Yanhui, 2021. "High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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    Cited by:

    1. Zhang, J. & Liu, X., 2022. "Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D," Applied Mathematics and Computation, Elsevier, vol. 432(C).

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