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.

翻译：本文提出了一种新颖的交错间断伽辽金（SDG）方法，专为在多面体网格上求解椭圆型方程而设计。该方法采用原始-对偶网格框架，以确保通量的局部守恒性，从而显著提升稳定性和精度。该方法是可杂交化的，与现有方法相比减少了自由度数量。同时，该方法也建立了与多面体网格上其他数值方法之间的联系。数值实验验证了该方法的最优收敛速率和计算效率。