TY - JOUR
T1 - Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
AU - Hong , Qingguo
AU - Xu , Jinchao
JO - Journal of Computational Mathematics
VL - 2
SP - 283
EP - 310
PY - 2020
DA - 2020/11
SN - 39
DO - http://doi.org/10.4208/jcm.2003-m2018-0223
UR - https://global-sci.org/intro/article_detail/jcm/18375.html
KW - Uniform Stability, Uniform Error Estimate, Hybrid Discontinuous Galerkin, Weak Galerkin.
AB - <p style="text-align: justify;">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 converges to a mixed
conforming method.</p>