Scholarlink

<p>This study presents a virtual element method with streamline upwind Petrov-Galerkin stabilization for the Sobolev equation in the convection-dominated regime. We formulate both semi-discrete and fully discrete schemes, using the Backward Euler method for time discretization. A priori error estimates are established for both the schemes, showing optimal convergence rates depending on mesh size, time step, and problem parameters under suitable conditions on the local stabilization parameter. The error bounds remain robust even with small diffusion coefficients relative to convection terms. Numerical experiments validate the theoretical results, demonstrating the method’s ability to capture solution features accurately without spurious oscillations in challenging cases, including boundary and internal layers.</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

SUPG-Stabilized Virtual Element Methods for the Sobolev Equation with Convection-Dominated Term on Polygonal Meshes

  • 期刊论文

  • 发表日期：

    2026年6月24日

查看全文
  • Ankit Kumar,
  • Sangita Yadav,
  • Sarvesh Kumar

摘要

This study presents a virtual element method with streamline upwind Petrov-Galerkin stabilization for the Sobolev equation in the convection-dominated regime. We formulate both semi-discrete and fully discrete schemes, using the Backward Euler method for time discretization. A priori error estimates are established for both the schemes, showing optimal convergence rates depending on mesh size, time step, and problem parameters under suitable conditions on the local stabilization parameter. The error bounds remain robust even with small diffusion coefficients relative to convection terms. Numerical experiments validate the theoretical results, demonstrating the method’s ability to capture solution features accurately without spurious oscillations in challenging cases, including boundary and internal layers.