| INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS |
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| 引用本文： | 侯延仁. INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS[J]. 数学物理学报(B辑英文版), 2003, 23(2): 219-238. DOI: 10.1016/S0252-9602(17)30226-6 |
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| 作者姓名： | 侯延仁 |
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| 作者单位： | College of Science，Xi'an Jiaotong University，Department of Mathematics and Computing Science Xi'an 710049，ChinaR.M.M. Mattheij，Eindhoven University of Technology P.O. Box 513，5600 MB Eindhoven，The Netherlands |
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| 基金项目： | Subsidized by the Special Funds for Major State Basic Research ProjectsG1999032801-07,NSFC(10101020,10001028)，Tian Yuan Funds(TY10126004) |
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| 摘 要： | Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper.
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| 收稿时间： | 2000-06-06 |
INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS |
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| R.M.M.Mattheij. INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS[J]. Acta Mathematica Scientia, 2003, 23(2): 219-238. DOI: 10.1016/S0252-9602(17)30226-6 |
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| Authors: | R.M.M.Mattheij |
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| Affiliation: | 1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China;2. Institute of Mathematics and Physics, Xinjiang University, Urumqi 830046, China;3. School of Mathematics and Statistics, Xi''an Jiaotong University, Xi''an 710049, China |
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| Abstract: | Several kind of new numerical schemes for the stationary Navier-Stokes equations based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are presented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper. |
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| Keywords: | Navier-Stokes equations error estimation inertial algorithms |
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