![](/images/graphics-bg.png)
A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations
Joint Authors
Di, Zhenhua
Xie, Dongxiu
Li, Jian
Tian, Xiangjun
Wang, Aiwen
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-19, 19 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-10-20
Country of Publication
Egypt
No. of Pages
19
Main Subjects
Abstract EN
A reduced stabilized mixed finite-element (RSMFE) formulation based on proper orthogonal decomposition (POD) for the transient Navier-Stokes equations is presented.
An ensemble of snapshots is compiled from the transient solutions derived from a stabilized mixed finite-element (SMFE) method based on two local Gauss integrations for the two-dimensional transient Navier-Stokes equations by using the lowest equal-order pair of finite elements.
Then, the optimal orthogonal bases are reconstructed by implementing POD techniques for the ensemble snapshots.
Combining POD with the SMFE formulation, a new low-dimensional and highly accurate SMFE method for the transient Navier-Stokes equations is obtained.
The RSMFE formulation could not only greatly reduce its degrees of freedom but also circumvent the constraint of inf-sup stability condition.
Error estimates between the SMFE solutions and the RSMFE solutions are derived.
Numerical tests confirm that the errors between the RSMFE solutions and the SMFE solutions are consistent with the the theoretical results.
Conclusion can be drawn that RSMFE method is feasible and efficient for solving the transient Navier-Stokes equations.
American Psychological Association (APA)
Wang, Aiwen& Li, Jian& Di, Zhenhua& Tian, Xiangjun& Xie, Dongxiu. 2011. A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-19.
https://search.emarefa.net/detail/BIM-506188
Modern Language Association (MLA)
Wang, Aiwen…[et al.]. A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations. Mathematical Problems in Engineering No. 2011 (2011), pp.1-19.
https://search.emarefa.net/detail/BIM-506188
American Medical Association (AMA)
Wang, Aiwen& Li, Jian& Di, Zhenhua& Tian, Xiangjun& Xie, Dongxiu. A New Reduced Stabilized Mixed Finite-Element Method Based on Proper Orthogonal Decomposition for the Transient Navier-Stokes Equations. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-19.
https://search.emarefa.net/detail/BIM-506188
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506188