A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes

TL;DR

This paper presents a new staggered discontinuous Galerkin method for elliptic equations on polytopal meshes, emphasizing local flux conservation, stability, and efficiency, validated through numerical experiments.

Contribution

It introduces a primal staggered DG method with a primal-dual grid framework that enhances stability, accuracy, and reduces degrees of freedom on polytopal meshes.

Findings

Achieves optimal convergence rates

Demonstrates improved stability and accuracy

Reduces degrees of freedom compared to existing methods

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. Numerical experiments validate the method's optimal convergence rates and computational efficiency.