| ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS |
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| 作者姓名： | Ali I.Nesliturk |
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| 作者单位： | Department of Mathematics, Izmir Institute of Technology, P.O. Box 35430, Izmir, Turkey |
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| 摘 要： | This paper considers the Calerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble （RFB） functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements.
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| 关 键 词： | Galerkin有限元分析 Navier-Stokes方程 稳定性 RFB函数 |
| 收稿时间： | 2003-07-28 |
| 修稿时间： | 2004-08-14 |
ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS |
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| Ali I.Nesliturk.ON THE STABILITY OF THE RESIDUAL-FREE BUBBLES FOR THE NAVIER-STOKES EQUATIONS[J].Acta Mathematica Scientia,2005,25(4):715-730. |
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| Authors: | Ali I Nesliturk |
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| Institution: | 1. Kobayashi–Maskawa Institute for the Origin of Particles and the Universe (KMI), Nagoya University, Nagoya 464-8602, Japan;2. Department of Physics, Nagoya University, Nagoya 464-8602, Japan;3. Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany;1. Department of Mathematics and Computer Science, Emory University, Atlanta, GA 30322, USA;2. MATHICSE - Chair of Modelling and Scientific Computing (CMCS), EPFL, CH - 1015 Lausanne, Switzerland;1. Department of Mathematics, Korea Military Academy, 77-1 Gongneung-dong, Nowon-gu, Seoul, 01805, Republic of Korea;2. Department of Mathematics, Texas A&M University, College Station, TX 77843, USA;1. Department of Mathematics, The LNM Institute of Information Technology, Jaipur 302031, India;2. Department of Mathematics, Industrial Mathematics Group, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India;1. Department of Molecular, Cellular and Developmental Biology, Yale University, West Haven, CT 06516, USA;2. Systems Biology Institute, Yale University, West Haven, CT 06516, USA;3. Department of Computer Science, KU Leuven, 3001 Leuven, Belgium;4. Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08544, USA;5. Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA |
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| Abstract: | This paper considers the Galerkin finite element method for the incompressible Navier-Stokes equations in two dimensions, where the finite-dimensional spaces employed consist of piecewise polynomials enriched with residual-free bubble (RFB) functions. The stability features of the residual-free bubble functions for the linearized Navier-Stokes equations are analyzed in this work. It is shown that the enrichment of the velocity space by bubble functions stabilizes the numerical method for any value of the viscosity parameter for triangular elements and for values of the viscosity parameter in the vanishing limit case for quadrilateral elements. |
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| Keywords: | Galerkin finite element method incompressible Navier-Stokes equations stability |
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