TY - JOUR
T1 - Analysis of a Two-Level Algorithm for HDG Methods for Diffusion Problems
AU - Binjie Li, Xiaoping Xie & Shiquan Zhang
JO - Communications in Computational Physics
VL - 5
SP - 1435
EP - 1460
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.scpde14.38s
UR - https://global-sci.org/intro/article_detail/cicp/11137.html
KW - 
AB - <p style="text-align: justify;">This paper analyzes an abstract two-level algorithm for hybridizable discontinuous
Galerkin (HDG) methods in a unified fashion. We use an extended version
of the Xu-Zikatanov (X-Z) identity to derive a sharp estimate of the convergence rate of
the 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 need
the minimal regularity of the model problem; the other is that we do not require the
triangulations to be quasi-uniform. Numerical experiments are provided to confirm
the theoretical results.</p>