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

Lina Zhao, Eun-Jae Park, Dong wook Shin

Research output: Contribution to journalArticle

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.

LanguageEnglish
Pages854-875
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume345
DOIs
Publication statusPublished - 2019 Mar 1

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mesh
polygons
Galerkin method
error analysis
Galerkin methods
regularity
estimators
Error analysis
partitions
flexibility
coverings
grids
Experiments
energy

All Science Journal Classification (ASJC) codes

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

Cite this

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A staggered DG method of minimal dimension for the Stokes equations on general meshes. / Zhao, Lina; Park, Eun-Jae; Shin, Dong wook.

In: Computer Methods in Applied Mechanics and Engineering, Vol. 345, 01.03.2019, p. 854-875.

Research output: Contribution to journalArticle

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