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<p>In this paper, a nonsymmetric interior penalty Galerkin (NIPG) method is proposed on Bakhvalov-type meshes for solving a singularly perturbed convection-diffusion problem with a discontinuous source term. Specifically, a Gauß Lobatto projection is employed within the boundary layers, while a Gauß Radau projection is adopted in the outer regions of the layers. Based on this hybrid projection strategy, an optimal-order uniform convergence result is rigorously derived under the energy norm. Finally, comprehensive numerical experiments are conducted to verify the correctness and effectiveness of the theoretical findings.</p>

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Uniformly convergent NIPG methods for solving singularly perturbed convection-diffusion equations with a discontinuous source term

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Ke Liu,
  • Li-Bin Liu

摘要

In this paper, a nonsymmetric interior penalty Galerkin (NIPG) method is proposed on Bakhvalov-type meshes for solving a singularly perturbed convection-diffusion problem with a discontinuous source term. Specifically, a Gauß Lobatto projection is employed within the boundary layers, while a Gauß Radau projection is adopted in the outer regions of the layers. Based on this hybrid projection strategy, an optimal-order uniform convergence result is rigorously derived under the energy norm. Finally, comprehensive numerical experiments are conducted to verify the correctness and effectiveness of the theoretical findings.