Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

Shao Chun Chen; Li Na Dong; Zhonghua Qiao

doi:10.1007/s11425-013-4692-z

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

Shao Chun Chen, Li Na Dong, Zhonghua Qiao

Research output: Journal article publication › Journal article › Academic research › peer-review

13 Citations (Scopus)

Abstract

We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)-conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.

Original language	English
Pages (from-to)	2723-2736
Number of pages	14
Journal	Science China Mathematics
Volume	56
Issue number	12
DOIs	https://doi.org/10.1007/s11425-013-4692-z
Publication status	Published - 25 Jul 2013

Keywords

Darcy-Stokes problem
H(div)-conforming rectangular elements
uniform convergence

ASJC Scopus subject areas

General Mathematics

More information

10.1007/s11425-013-4692-z

Cite this

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title = "Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem",

abstract = "We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)-conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.",

keywords = "Darcy-Stokes problem, H(div)-conforming rectangular elements, uniform convergence",

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AU - Chen, Shao Chun

AU - Dong, Li Na

AU - Qiao, Zhonghua

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Y1 - 2013/7/25

N2 - We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)-conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.

AB - We consider a singular perturbation problem which describes 2D Darcy-Stokes flow. An H(div)-conforming rectangular element, DS-R14, is proposed and analyzed first. This element has 14 degrees of freedom for velocity and is proved to be uniformly convergent with respect to perturbation constant. We then simplify this element to get another H(div)-conforming rectangular element, DS-R12, which has 12 degrees of freedom for velocity. The uniform convergence is also obtained for this element. Finally, we construct a de Rham complex corresponding to DS-R12 element.

KW - Darcy-Stokes problem

KW - H(div)-conforming rectangular elements

KW - uniform convergence

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DO - 10.1007/s11425-013-4692-z

M3 - Journal article

SN - 1674-7283

VL - 56

SP - 2723

EP - 2736

JO - Science China Mathematics

JF - Science China Mathematics

IS - 12

ER -

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

Abstract

Keywords

ASJC Scopus subject areas

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