Analysis of a two-level algorithm for HDG methods for diffusion problems
Numerical Analysis
2016-06-29 v1
Abstract
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 apply 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.
Cite
@article{arxiv.1502.04371,
title = {Analysis of a two-level algorithm for HDG methods for diffusion problems},
author = {Binjie Li and Xiaoping Xie and Shiquan Zhang},
journal= {arXiv preprint arXiv:1502.04371},
year = {2016}
}