Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
Numerical Analysis
2018-10-09 v2
Abstract
In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converge to a mixed conforming method.
Keywords
Cite
@article{arxiv.1805.09670,
title = {Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods},
author = {Qingguo Hong and Jinchao Xu},
journal= {arXiv preprint arXiv:1805.09670},
year = {2018}
}
Comments
31 pages. arXiv admin note: text overlap with arXiv:1712.01211