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High-order finite element method on a Bakhvalov-type mesh for a singularly perturbed convection–diffusion problem with two parameters

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  • Zhang, Jin
  • Lv, Yanhui

Abstract

We investigate in this article convergence for a kth(k≥2) order finite element method on a Bakhvalov-type mesh for a two-parameter singularly perturbed two-point boundary value problem. By means of a special interpolation, we obtain the errors for Lagrange interpolation, and then prove the optimal order of convergence. Numerical experiments are given to demonstrate the theoretical results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:397:y:2021:i:c:s0096300321000011
    DOI: 10.1016/j.amc.2021.125953
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    Cited by:

    1. Lv, Yanhui & Zhang, Jin, 2022. "Convergence and supercloseness of a finite element method for a two-parameter singularly perturbed problem on Shishkin triangular mesh," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    2. 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.
    3. Lv, Yanhui & Zhang, Jin, 2022. "Analysis of finite element method in balanced norms for two-parameter singularly perturbed problems," Applied Mathematics and Computation, Elsevier, vol. 431(C).

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