A staggered cell-centered dg method for linear elasticity on polygonal meshes

Lina Zhao; Eun Jae Park

doi:10.1137/19M1278016

A staggered cell-centered dg method for linear elasticity on polygonal meshes

Lina Zhao, Eun Jae Park

Department of Computational Science and Engineering

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted. There are three unknowns involved in our formulation: stress, displacement, and rotation. The continuities of the three unknowns are staggered on the interelement boundaries. In addition, the symmetry of the stress tensor is imposed weakly by the introduction of Lagrange multipliers. Optimal a priori error estimates covering low regularities in L² errors of stress, displacement, and rotation are given; in addition, the locking-free error estimates are also investigated. Numerical experiments confirm the theoretical findings and verify the flexibility to rough grids and the locking-free property of the proposed method.

Original language	English
Pages (from-to)	A2158-A2181
Journal	SIAM Journal on Scientific Computing
Volume	42
Issue number	4
DOIs	https://doi.org/10.1137/19M1278016
Publication status	Published - 2020

Bibliographical note

Funding Information:
\ast Submitted to the journal's Methods and Algorithms for Scientific Computing section July 29, 2019; accepted for publication (in revised form) April 21, 2020; published electronically July 14, 2020. https://doi.org/10.1137/19M1278016 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT through grants NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021. \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR (lzhao@math.cuhk.edu.hk). \ddagger Department of Computational Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea (ejpark@yonsei.ac.kr).

Funding Information:
The work of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT through grants NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021.

Publisher Copyright:
© 2020 Society for Industrial and Applied Mathematics

All Science Journal Classification (ASJC) codes

Computational Mathematics
Applied Mathematics

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10.1137/19M1278016

Cite this

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title = "A staggered cell-centered dg method for linear elasticity on polygonal meshes",

abstract = "We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted. There are three unknowns involved in our formulation: stress, displacement, and rotation. The continuities of the three unknowns are staggered on the interelement boundaries. In addition, the symmetry of the stress tensor is imposed weakly by the introduction of Lagrange multipliers. Optimal a priori error estimates covering low regularities in L2 errors of stress, displacement, and rotation are given; in addition, the locking-free error estimates are also investigated. Numerical experiments confirm the theoretical findings and verify the flexibility to rough grids and the locking-free property of the proposed method.",

author = "Lina Zhao and Park, {Eun Jae}",

note = "Funding Information: \ast Submitted to the journal's Methods and Algorithms for Scientific Computing section July 29, 2019; accepted for publication (in revised form) April 21, 2020; published electronically July 14, 2020. https://doi.org/10.1137/19M1278016 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : The work of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT through grants NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021. \dagger Department of Mathematics, The Chinese University of Hong Kong, Hong Kong SAR (lzhao@math.cuhk.edu.hk). \ddagger Department of Computational Science and Engineering, Yonsei University, Seoul 03722, Republic of Korea (ejpark@yonsei.ac.kr). Funding Information: The work of the second author was supported by a National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT through grants NRF-2015R1A5A1009350 and NRF-2019R1A2C2090021. Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics",

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PY - 2020

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N2 - We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted. There are three unknowns involved in our formulation: stress, displacement, and rotation. The continuities of the three unknowns are staggered on the interelement boundaries. In addition, the symmetry of the stress tensor is imposed weakly by the introduction of Lagrange multipliers. Optimal a priori error estimates covering low regularities in L2 errors of stress, displacement, and rotation are given; in addition, the locking-free error estimates are also investigated. Numerical experiments confirm the theoretical findings and verify the flexibility to rough grids and the locking-free property of the proposed method.

AB - We develop a new numerical method, namely, a locking-free staggered cell-centered discontinuous Galerkin method for linear elasticity on fairly general meshes. The method is well suited for general meshes possibly including hanging nodes; in particular, it does not deteriorate when the mesh becomes highly distorted. There are three unknowns involved in our formulation: stress, displacement, and rotation. The continuities of the three unknowns are staggered on the interelement boundaries. In addition, the symmetry of the stress tensor is imposed weakly by the introduction of Lagrange multipliers. Optimal a priori error estimates covering low regularities in L2 errors of stress, displacement, and rotation are given; in addition, the locking-free error estimates are also investigated. Numerical experiments confirm the theoretical findings and verify the flexibility to rough grids and the locking-free property of the proposed method.

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A staggered cell-centered dg method for linear elasticity on polygonal meshes

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