A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes

2024/10/31 by Long Chen, Xinquan Huang, Chen, L. +5
Engineering · #Advanced Numerical Analysis Techniques #Advanced machining processes and optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering

paper · pdf · doi:10.48550/arxiv.2410.23865

openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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