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<p>In this paper a numerical method on a posteriori mesh is presented to solve a second-order singularly perturbed convection-diffusion equation. A second-order three-point difference method is used to discretize the singularly perturbed convection-diffusion equation. A posteriori error analysis involving simple calculations with fewer proof techniques is developed for the second-order three-point difference method on an arbitrary mesh. A solution-adaptive algorithm based on a posteriori error analysis is designed to generate a posteriori mesh and the approximation solution. Numerical experiments verify the second-order uniform convergence of this method.</p>

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A simplified a posteriori error analysis of a second-order difference scheme for a singularly perturbed convection-diffusion problem

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Jian Huang,
  • Zhongdi Cen,
  • Aimin Xu

摘要

In this paper a numerical method on a posteriori mesh is presented to solve a second-order singularly perturbed convection-diffusion equation. A second-order three-point difference method is used to discretize the singularly perturbed convection-diffusion equation. A posteriori error analysis involving simple calculations with fewer proof techniques is developed for the second-order three-point difference method on an arbitrary mesh. A solution-adaptive algorithm based on a posteriori error analysis is designed to generate a posteriori mesh and the approximation solution. Numerical experiments verify the second-order uniform convergence of this method.