Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations

Jie Du Yau Mathematical Sciences Center, Tsinghua University, Beijing, China Eric T. Chung Department of Mathematics, The Chinese University of Hong Kong, Sha Tin, Hong Kong SAR Ming Fai Lam Department of Mathematics, The Chinese University of Hong Kong, Sha Tin, Hong Kong SAR Xiao-Ping Wang Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong SAR

Numerical Analysis and Scientific Computing mathscidoc:2205.25020

Journal of Scientific Computing, 76, 1547–1577, 2018.3
In this paper, we present a discontinuous Galerkin method with staggered hybridization to discretize a class of nonlinear Stokes equations in two dimensions. The utilization of staggered hybridization is new and this approach combines the features of traditional hybridization method and staggered discontinuous Galerkin method. The main idea of our method is to use hybrid variables to impose the staggered continuity conditions instead of enforcing them in the approximation space. Therefore, our method enjoys some distinctive advantages, including mass conservation, optimal convergence and preservation of symmetry of the stress tensor. We will also show that, one can obtain superconvergent and strongly divergence-free velocity by applying a local postprocessing technique on the approximate solution. We will analyze the stability and derive a priori error estimates of the proposed scheme. The resulting nonlinear system is solved by using the Newton’s method, and some numerical results will be demonstrated to confirm the theoretical rates of convergence and superconvergence.
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@inproceedings{jie2018discontinuous,
  title={Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations},
  author={Jie Du, Eric T. Chung, Ming Fai Lam, and Xiao-Ping Wang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520152345791303310},
  booktitle={Journal of Scientific Computing},
  volume={76},
  pages={1547–1577},
  year={2018},
}
Jie Du, Eric T. Chung, Ming Fai Lam, and Xiao-Ping Wang. Discontinuous Galerkin Method with Staggered Hybridization for a Class of Nonlinear Stokes Equations. 2018. Vol. 76. In Journal of Scientific Computing. pp.1547–1577. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220520152345791303310.
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