Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems (Communications in Computational Physics, 2020)
This paper analyzes an abstract two-level algorithm for hybridizable discontinuousGalerkin (HDG) methods in a unified fashion. We use an extended versionof the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate ofthe algorithm, and show that the theoretical results also are applied to weak Galerkin(WG) methods. The main features of our analysis are twofold: one is that we only needthe minimal regularity of the model problem; the other is that we do not require thetriangulations to be quasi-uniform. Numerical experiments are provided to confirmthe theoretical results.