A staggered DG method of minimal dimension for the Stokes equations on general meshes

Lina Zhao; Eun Jae Park; Dong wook Shin

doi:10.1016/j.cma.2018.11.016

A staggered DG method of minimal dimension for the Stokes equations on general meshes

Lina Zhao, Eun Jae Park, Dong wook Shin

Department of Computational Science and Engineering

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

17 Citations (Scopus)

Abstract

In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L² error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.

Original language	English
Pages (from-to)	854-875
Number of pages	22
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	345
DOIs	https://doi.org/10.1016/j.cma.2018.11.016
Publication status	Published - 2019 Mar 1

Bibliographical note

Funding Information:
This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358.This author was supported by National Institute for Mathematical Sciences (NIMS) grant funded by the Korea government (MSIT) (No. B18310000) and NRF -2017R1D1A1B03035708.

Publisher Copyright:
© 2018 Elsevier B.V.

All Science Journal Classification (ASJC) codes

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
Physics and Astronomy(all)
Computer Science Applications

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10.1016/j.cma.2018.11.016

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title = "A staggered DG method of minimal dimension for the Stokes equations on general meshes",

abstract = "In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.",

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AU - Zhao, Lina

AU - Park, Eun Jae

AU - Shin, Dong wook

N1 - Funding Information: This author was supported by NRF-2015R1A5A1009350 and NRF-2016R1A2B4014358.This author was supported by National Institute for Mathematical Sciences (NIMS) grant funded by the Korea government (MSIT) (No. B18310000) and NRF -2017R1D1A1B03035708. Publisher Copyright: © 2018 Elsevier B.V.

PY - 2019/3/1

Y1 - 2019/3/1

N2 - In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.

AB - In this paper, a locally conservative, lowest order staggered discontinuous Galerkin method is developed for the Stokes equations. The proposed method allows rough grids and is based on the partition of the domain into arbitrary shapes of quadrilaterals or polygons, which makes the method highly desirable for practical applications. A priori error analysis covering low regularity is demonstrated. A new postprocessing scheme for the velocity earning faster convergence is constructed. Next, adaptive mesh refinement is highly appreciated on quadrilateral and polygonal meshes since hanging nodes are allowed. Therefore, we propose two guaranteed-type error estimators in L2 error of stress and energy error of the postprocessed velocity, respectively. Numerical experiments confirm our theoretical findings and illustrate the flexibility of the proposed method and accuracy of the guaranteed upper bounds.

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JO - Computer Methods in Applied Mechanics and Engineering

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A staggered DG method of minimal dimension for the Stokes equations on general meshes

Abstract

Bibliographical note

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