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

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...

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Bibliographic Details
Published in:Science China. Mathematics 2013-12, Vol.56 (12), p.2723-2736
Main Authors: Chen, ShaoChun, Dong, LiNa, Qiao, ZhongHua
Format: Article
Language:English
Subjects:
Applications of Mathematics
Astronomy
China
Constants
Construction
Convergence
Degrees of freedom
Mathematical analysis
Mathematics
Mathematics and Statistics
Perturbation methods
Series (mathematics)
Singular perturbation
Two dimensional
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Summary: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.
ISSN:1674-7283
1006-9283
1869-1862
DOI:10.1007/s11425-013-4692-z