Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods

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.

Author Details

Qingguo Hong

Jinchao Xu

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