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<p>This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid framework to ensure local conservation of fluxes, significantly improving stability and accuracy. The method is hybridizable and reduces the degrees of freedom compared to existing approaches. It also bridges connections to other numerical methods on polytopal meshes. In particular, it can be interpreted as a stabilization-free weak Galerkin method or stabilization-free non-conforming virtual element method. Numerical experiments validate the method’s optimal convergence rates, computational efficiency, and local conservation property.</p>

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A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes

  • 期刊论文

  • 发表日期：

    2025年7月26日

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  • Long Chen,
  • Xuehai Huang,
  • Eun-Jae Park,
  • Ruishu Wang

摘要

This paper introduces a novel staggered discontinuous Galerkin (SDG) method tailored for solving elliptic equations on polytopal meshes. Our approach utilizes a primal-dual grid framework to ensure local conservation of fluxes, significantly improving stability and accuracy. The method is hybridizable and reduces the degrees of freedom compared to existing approaches. It also bridges connections to other numerical methods on polytopal meshes. In particular, it can be interpreted as a stabilization-free weak Galerkin method or stabilization-free non-conforming virtual element method. Numerical experiments validate the method’s optimal convergence rates, computational efficiency, and local conservation property.