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A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS
Alternative TitleA STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS
Tian Wanfu1; Song Liqiu2; Li Yonghai3
2012
Source PublicationJOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN0254-9409
Volume30Issue:6Pages:615-628
AbstractWe construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H-1 norm and the pressure in the L-2 norm. In addition, a second order optimal error estimate for the velocity in the L-2 norm is derived. Numerical experiments illustrating the theoretical results are included.
Other AbstractWe construct a new stabilized finite volume method on rectangular grids for the Stokes equations. The lowest equal-order conforming finite element pair (piecewise bilinear velocities and pressures) and piecewise constant test spaces for both the velocity and pressure are employed in this method. We show the stability of this method and prove first optimal rate of convergence for the velocity in the H~1 norm and the pressure in the L~2 norm. In addition, a second order optimal error estimate for the velocity in the L~2 norm is derived. Numerical experiments illustrating the theoretical results are included.
KeywordGENERALIZED DIFFERENCE-METHODS ELEMENT METHODS INCOMPRESSIBLE-FLOW COVOLUME METHOD Stokes equations Equal-order finite element pair Finite volume method Error estimate
Indexed ByCSCD
Language英语
Funding Project[985 program of Jilin University] ; [National Natural Science Foundation of China]
CSCD IDCSCD:4707995
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Document Type期刊论文
Identifierhttp://ir.imr.ac.cn/handle/321006/150262
Collection中国科学院金属研究所
Affiliation1.中国科学院金属研究所
2.中山大学
3.吉林大学
Recommended Citation
GB/T 7714
Tian Wanfu,Song Liqiu,Li Yonghai. A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2012,30(6):615-628.
APA Tian Wanfu,Song Liqiu,&Li Yonghai.(2012).A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS.JOURNAL OF COMPUTATIONAL MATHEMATICS,30(6),615-628.
MLA Tian Wanfu,et al."A STABILIZED EQUAL-ORDER FINITE VOLUME METHOD FOR THE STOKES EQUATIONS".JOURNAL OF COMPUTATIONAL MATHEMATICS 30.6(2012):615-628.
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