A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

Yunzhang Zhang; Yanren Hou; Haibiao Zheng

doi:10.1002/num.21811

A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

Yunzhang Zhang^*, Yanren Hou, Haibiao Zheng

^*Corresponding author for this work

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

29 Scopus citations

Abstract

In this article, supposing that the velocity, pressure, and temperature are approximated by the elements P2-P1-P2, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the common variational multiscale (VMS) method and derive a new VMS (Two Gauss VMS) method for steady-state natural convection problem. Comparing with the common VMS method, the Two Gauss VMS method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. The effectiveness and stability of the Two Gauss VMS method are further demonstrated through two numerical examples. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 361-375, 2014

Original language	English
Pages (from-to)	361-375
Number of pages	15
Journal	Numerical Methods for Partial Differential Equations
Volume	30
Issue number	2
DOIs	https://doi.org/10.1002/num.21811
State	Published - Mar 2014
Externally published	Yes

Keywords

finite element method
natural convection problem
two local gauss integrations
variational multiscale method

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10.1002/num.21811

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title = "A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations",

abstract = "In this article, supposing that the velocity, pressure, and temperature are approximated by the elements P2-P1-P2, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the common variational multiscale (VMS) method and derive a new VMS (Two Gauss VMS) method for steady-state natural convection problem. Comparing with the common VMS method, the Two Gauss VMS method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. The effectiveness and stability of the Two Gauss VMS method are further demonstrated through two numerical examples. {\textcopyright} 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 361-375, 2014",

keywords = "finite element method, natural convection problem, two local gauss integrations, variational multiscale method",

author = "Yunzhang Zhang and Yanren Hou and Haibiao Zheng",

year = "2014",

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doi = "10.1002/num.21811",

language = "英语",

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pages = "361--375",

journal = "Numerical Methods for Partial Differential Equations",

issn = "0749-159X",

publisher = "John Wiley \& Sons Inc.",

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TY - JOUR

T1 - A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

AU - Zhang, Yunzhang

AU - Hou, Yanren

AU - Zheng, Haibiao

PY - 2014/3

Y1 - 2014/3

N2 - In this article, supposing that the velocity, pressure, and temperature are approximated by the elements P2-P1-P2, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the common variational multiscale (VMS) method and derive a new VMS (Two Gauss VMS) method for steady-state natural convection problem. Comparing with the common VMS method, the Two Gauss VMS method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. The effectiveness and stability of the Two Gauss VMS method are further demonstrated through two numerical examples. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 361-375, 2014

AB - In this article, supposing that the velocity, pressure, and temperature are approximated by the elements P2-P1-P2, and applying the orthogonal projection technique, we introduce two Gauss integrations as a stabilizing term in the common variational multiscale (VMS) method and derive a new VMS (Two Gauss VMS) method for steady-state natural convection problem. Comparing with the common VMS method, the Two Gauss VMS method does not need to introduce any extra variable and reduces the degrees of freedom of the discrete system a lot, but gets the same stabilized result. The effectiveness and stability of the Two Gauss VMS method are further demonstrated through two numerical examples. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 361-375, 2014

KW - finite element method

KW - natural convection problem

KW - two local gauss integrations

KW - variational multiscale method

UR - https://www.scopus.com/pages/publications/84893645044

U2 - 10.1002/num.21811

DO - 10.1002/num.21811

M3 - 文章

AN - SCOPUS:84893645044

SN - 0749-159X

VL - 30

SP - 361

EP - 375

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

IS - 2

ER -

A finite element variational multiscale method for steady-state natural convection problem based on two local gauss integrations

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