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 language | English (US) |
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Pages (from-to) | 283-310 |
Number of pages | 28 |
Journal | Journal of Computational Mathematics |
Volume | 39 |
Issue number | 2 |
DOIs | |
State | Published - Jan 1 2020 |
Externally published | Yes |
Bibliographical note
Generated from Scopus record by KAUST IRTS on 2023-02-15ASJC Scopus subject areas
- Computational Mathematics