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A Superconvergent C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} Discontinuous Galerkin Method for Kirchhoff Plates: Error Estimates, Hybridization and Postprocessing

Authors
  • Huang, Xuehai1
  • Huang, Jianguo2, 3
  • 1 Wenzhou University, College of Mathematics and Information Science, Wenzhou, 325035, China , Wenzhou (China)
  • 2 Shanghai Jiao Tong University, School of Mathematical Sciences, MOE-LSC, Shanghai, 200240, China , Shanghai (China)
  • 3 Shanghai Normal University, Division of Computational Science, E-Institute of Shanghai Universities, Shanghai, China , Shanghai (China)
Type
Published Article
Journal
Journal of Scientific Computing
Publisher
Springer US
Publication Date
Jun 09, 2016
Volume
69
Issue
3
Pages
1251–1278
Identifiers
DOI: 10.1007/s10915-016-0232-7
Source
Springer Nature
Keywords
License
Yellow

Abstract

This paper is devoted to a superconvergent C0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C^0$$\end{document} discontinuous Galerkin (SCDG) method for Kirchhoff plates. First of all, following the ideas in Huang et al. (Comput Methods Appl Mech Eng 199(23–24):1446–1454, 2010) but with the normal bending moment and twisting moment as new numerical traces, we propose a modified framework of CDG methods for Kirchhoff plates. Then by a technical choice of the numerical traces, we obtain our SCDG method. Observing that the famous Hellan–Herrmann–Johnson (HHJ) method is a special case of the SCDG method, we are motivated to borrow some techniques for analyzing the HHJ method to derive optimal and superconvergent error estimates for the SCDG method. Under some assumption on the stabilization parameters, we consider the hybridization of the SCDG method. Furthermore, we construct a superconvergent discrete deflection by postprocessing the solution of the method using similar technique in Stenberg (RAIRO Modél Math Anal Numér 25(1):151–167, 1991). Some numerical results are performed to demonstrate the theoretical results for the SCDG method.

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