Staggered dg methods for the pseudostress-velocity formulation of the stokes equations on general meshes

Dohyun Kim, Lina Zhao, Eun Jae Park

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

In this paper, we introduce staggered discontinuous Galerkin methods for the stationary Stokes flow on polygonal meshes. The proposed method is based on the pseudostress-velocity formulation. A Lagrange multiplier on dual edges is introduced to impose the continuity of the pseudostress, which reduces the size of the final system via hybridization and eases the construction of the finite element space for the approximation of the pseudostress. The resulting method is stable and optimally convergent even on distorted or concave polygonal meshes. In addition, hanging nodes can be automatically incorporated in the construction of the method, which favors adaptive mesh refinement. Two types of local postprocessing for the velocity field are proposed to obtain one order higher convergence. Numerical experiments are provided to validate the theoretical findings and demonstrate the performance of the proposed method.

Original languageEnglish
Pages (from-to)A2537-A2560
JournalSIAM Journal on Scientific Computing
Volume42
Issue number4
DOIs
Publication statusPublished - 2020

Bibliographical note

Funding Information:
\ast Submitted to the journal's Methods and Algorithms for Scientific Computing section February 27, 2020; accepted for publication (in revised form) May 19, 2020; published electronically August 31, 2020. https://doi.org/10.1137/20M1322170 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the first author was supported by the Graduate School of YONSEI University Research Scholarship grants in 2019. The work of the third author was supported by the National Research Foundation of Korea (NRF) through grants by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021). \dagger Department of Computational Science and Engineering, Yonsei University, Seoul 03722, Korea (kim92n@yonsei.ac.kr, ejpark@yonsei.ac.kr). \ddagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong Special Administrative Region (lzhao@math.cuhk.edu.hk).

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics Publications. All rights reserved.

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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