Uniform stability and error analysis for some discontinuous galerkin methods

Qingguo Hong, Jinchao Xu

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)283-310
Number of pages28
JournalJournal of Computational Mathematics
Volume39
Issue number2
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Computational Mathematics

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