Submitted

A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes

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

Submitted

arXiv   Bibtex

ABSTRACT:

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 interpret as a stabilization-free weak Galerkin
method or stabilization-free non-conforming virtual element
method. Numerical experiments validate the method's optimal
convergence rates and computational efficiency.