Scholarlink

<p>In this paper, we develop a discontinuous Galerkin method for solving Volterra integro-differential equations with weakly singular kernels. To adapt the weak singularity of the solution, we construct an <i>hp</i>-version discontinuous Galerkin scheme based on fractional orthogonal polynomials, and derive <i>hp</i>-version error estimates over arbitrary meshes. Our analysis shows that, when the exponent of the weakly singular convolution kernel is a rational number, the proposed method attains <i>p</i>-version exponential convergence and exhibits no <i>h</i>-version order barrier. Numerical results confirm the validity of the method and support the theoretical findings.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fractional discontinuous Galerkin methods for Volterra integro-differential equations with weakly singular kernels

  • 期刊论文

  • 发表日期：

    2026年6月3日

查看全文
  • Yuchen Hua,
  • Chengming Huang

摘要

In this paper, we develop a discontinuous Galerkin method for solving Volterra integro-differential equations with weakly singular kernels. To adapt the weak singularity of the solution, we construct an hp-version discontinuous Galerkin scheme based on fractional orthogonal polynomials, and derive hp-version error estimates over arbitrary meshes. Our analysis shows that, when the exponent of the weakly singular convolution kernel is a rational number, the proposed method attains p-version exponential convergence and exhibits no h-version order barrier. Numerical results confirm the validity of the method and support the theoretical findings.