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A Superconvergent \(C^0\) Discontinuous Galerkin Method for Kirchhoff Plates: Error Estimates, Hybridization and Postprocessing

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Abstract

This paper is devoted to a superconvergent \(C^0\) 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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Acknowledgments

The authors would like to thank the referees for their valuable and insightful comments and suggestions, which greatly improved the early version of the paper. The work of the first author was partly supported by NSFC (Grant Nos. 11301396, 11171257) and Zhejiang Provincial Natural Science Foundation of China (LY14A010020, LY15A010015 and LY15A010016). The work of the second author was partly supported by NSFC (Grant Nos. 11171219, 11571237) and E-Institutes of Shanghai Municipal Education Commission (E03004).

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Authors and Affiliations

  1. College of Mathematics and Information Science, Wenzhou University, Wenzhou, 325035, China

    Xuehai Huang

  2. School of Mathematical Sciences, MOE-LSC, Shanghai Jiao Tong University, Shanghai, 200240, China

    Jianguo Huang

  3. Division of Computational Science, E-Institute of Shanghai Universities, Shanghai Normal University, Shanghai, China

    Jianguo Huang

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  1. Xuehai Huang
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Correspondence to Jianguo Huang.

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Huang, X., Huang, J. A Superconvergent \(C^0\) Discontinuous Galerkin Method for Kirchhoff Plates: Error Estimates, Hybridization and Postprocessing. J Sci Comput 69, 1251–1278 (2016). https://doi.org/10.1007/s10915-016-0232-7

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