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<p>In this paper a novel numerical method on a posteriori mesh is developed for solving a second-order singularly perturbed boundary value problem of convection-diffusion type. The second-order singularly perturbed boundary value problem is first transformed into a first-order parameterized singularly perturbed boundary value problem. Then a hybrid difference method on an arbitrary mesh is used to approximate the first-order parameterized singularly perturbed boundary value problem. The stability and a posteriori error analysis of the discretization method are derived. A solution-adaptive algorithm based on a posteriori error estimate is devised by equidistributing a monitor function. Numerical experiments reveal that the hybrid difference method on a posteriori mesh is second-order uniformly convergent.</p>

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A novel numerical method on a posteriori mesh for a singularly perturbed convection-diffusion boundary value problem

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Zhongdi Cen,
  • Jian Huang,
  • Aimin Xu

摘要

In this paper a novel numerical method on a posteriori mesh is developed for solving a second-order singularly perturbed boundary value problem of convection-diffusion type. The second-order singularly perturbed boundary value problem is first transformed into a first-order parameterized singularly perturbed boundary value problem. Then a hybrid difference method on an arbitrary mesh is used to approximate the first-order parameterized singularly perturbed boundary value problem. The stability and a posteriori error analysis of the discretization method are derived. A solution-adaptive algorithm based on a posteriori error estimate is devised by equidistributing a monitor function. Numerical experiments reveal that the hybrid difference method on a posteriori mesh is second-order uniformly convergent.