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<p>The local discontinuous Galerkin (LDG) method is used to solve a singularly perturbed convection–diffusion problem in one dimension. On two graded meshes, i.e., Duran–Shishkin and Duran meshes, we establish optimal-order error estimates of the LDG method in the energy norm, uniformly up to a logarithmic factor. Numerical experiments confirm the sharpness of our theoretical results.</p>

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The local discontinuous Galerkin method on graded meshes for 1d singularly perturbed convection–diffusion problems

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • You Wu,
  • Yao Cheng

摘要

The local discontinuous Galerkin (LDG) method is used to solve a singularly perturbed convection–diffusion problem in one dimension. On two graded meshes, i.e., Duran–Shishkin and Duran meshes, we establish optimal-order error estimates of the LDG method in the energy norm, uniformly up to a logarithmic factor. Numerical experiments confirm the sharpness of our theoretical results.