1. Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
- Author
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Qingguo Hong and Jinchao Xu
- Subjects
65N30, 65M60, 65M12 ,Discretization ,05 social sciences ,Numerical Analysis (math.NA) ,030204 cardiovascular system & hematology ,Stability (probability) ,03 medical and health sciences ,Computational Mathematics ,0302 clinical medicine ,Error analysis ,Discontinuous Galerkin method ,0502 economics and business ,Convergence (routing) ,FOS: Mathematics ,Applied mathematics ,050211 marketing ,Mathematics - Numerical Analysis ,Limit (mathematics) ,Galerkin method ,Mathematics - 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 converge to a mixed conforming method., 31 pages. arXiv admin note: text overlap with arXiv:1712.01211
- Published
- 2021