Journal of the Korean Society for Industrial and Applied Mathematics

Korean Society for Industrial and Applied Mathematics (한국산업응용수학회)
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REVIEW AND IMPLEMENTATION OF STAGGERED DG METHODS ON POLYGONAL MESHES

  • KIM, DOHYUN (SCHOOL OF MATHEMATICS AND COMPUTING (COMPUTATIONAL SCIENCE AND ENGINEERING), YONSEI UNIVERSITY) ;
  • ZHAO, LINA (DEPARTMENT OF MATHEMATICS, CITY UNIVERSITY OF HONG KONG) ;
  • PARK, EUN-JAE (SCHOOL OF MATHEMATICS AND COMPUTING (COMPUTATIONAL SCIENCE AND ENGINEERING), YONSEI UNIVERSITY)
  • Received : 2021.08.06
  • Accepted : 2021.09.23
  • Published : 2021.09.25
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Abstract

In this paper, we review the lowest order staggered discontinuous Galerkin methods on polygonal meshes in 2D. The proposed method offers many desirable features including easy implementation, geometrical flexibility, robustness with respect to mesh distortion and low degrees of freedom. Discrete function spaces for locally H1 and H(div) spaces are considered. We introduce special properties of a sub-mesh from a given star-shaped polygonal mesh which can be utilized in the construction of discrete spaces and implementation of the staggered discontinuous Galerkin method. For demonstration purposes, we consider the lowest case for the Poisson equation. We emphasize its efficient computational implementation using only geometrical properties of the underlying mesh.

Keywords

Acknowledgement

The research of EJP was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021).

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