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<p>In this article, we apply the Direct Discontinuous Galerkin (DDG) method to compute the numerical solution of two-parameter singularly perturbed convection–diffusion–reaction boundary value problems. We establish the consistency, stability, and convergence of order <i>k</i> (up to a logarithmic factor) in an energy-type norm, where <i>k</i> represents the polynomial degree in the finite element space. Our theoretical findings are validated through numerical experiments.</p>

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Analysis of two-parameter singular perturbation problems via the DDG method on Shishkin mesh

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Amit Yadav,
  • Gautam Singh

摘要

In this article, we apply the Direct Discontinuous Galerkin (DDG) method to compute the numerical solution of two-parameter singularly perturbed convection–diffusion–reaction boundary value problems. We establish the consistency, stability, and convergence of order k (up to a logarithmic factor) in an energy-type norm, where k represents the polynomial degree in the finite element space. Our theoretical findings are validated through numerical experiments.