Year: 2021
Author: Qingguo Hong, Jinchao Xu
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 283–310
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 converges to a mixed conforming method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2003-m2018-0223
Journal of Computational Mathematics, Vol. 39 (2021), Iss. 2 : pp. 283–310
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 28
Keywords: Uniform Stability Uniform Error Estimate Hybrid Discontinuous Galerkin Weak Galerkin.
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