| 平面定常Navier-Stokes方程组的有限元方法 |
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| 引用本文： | 王鸣,张鸿庆.平面定常Navier-Stokes方程组的有限元方法[J].大连理工大学学报,1986(Z1). |
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| 作者姓名： | 王鸣 张鸿庆 |
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| 作者单位： | 大连工学院应用数学研究所
(王鸣)，大连工学院应用数学研究所(张鸿庆) |
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| 摘 要： | 本文讨论平面定常流函数Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组的有限元方法及其收敛性，并且证明： 只要有限元空间具有逼近性，紧致性且通过广义分片检验，则当Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组的 解是唯一时，有限元解是收敛的；特珠地，本文证明了：用收敛的薄板弯曲单元求解这一 方程也是收敛的；进一步，当雷诺数足够小，Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程组的解的正则性满足薄 板弯曲时解的正则性要求时，有限元解的误差关于ｈｒ的量级与薄板弯曲的情形是一致的。
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| 关 键 词： | Navier-Stokes方程组 流函数 有限元方法 非协调元 拟协调元 |
Finite Element Methods for the Stationary Navier-Stokes Equations in the Stream Function Formulation |
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| Wang Ming,Zhang Hongqing.Finite Element Methods for the Stationary Navier-Stokes Equations in the Stream Function Formulation[J].Journal of Dalian University of Technology,1986(Z1). |
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| Authors: | Wang Ming Zhang Hongqing |
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| Abstract: | This paper is devoted to the finite element methods for the stationary Navier-Stokes equations in the stream function formulation. It is shown that the solu-tions of finite element equations are convergent when the solution of Navier-Stokes equation is unique, provided the finite element spaces have the approximability and the compactness and pass the generalized patch test.Specially, it is true that the finite elements, which are convergent for the bending pr-oblems of thin plate, are also convergent, and the error bounds are the same as that of thin plate bending problems with the same requirements of the regularity of the solutions to approximate. |
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| Keywords: | Navier-Stokes equation stream function finite element met- hod nonconforming element quasi-conforming element |
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