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| Navier-Stokes方程的一种等阶稳定化亏量校正有限元法 | |
| 引用本文： | 覃燕梅,冯民富,尹蕾.Navier-Stokes方程的一种等阶稳定化亏量校正有限元法[J].计算数学,2010,32(1):1-14. |
| 作者姓名： | 覃燕梅 冯民富 尹蕾 |
| 作者单位： | 1. 四川省高等学校数值仿真重点实验室,四川内江,1641112;内江师范学院数学系,四川内江,641112;四川大学数学学院,成都,610064 2. 四川大学数学学院,成都,610064 |
| 摘 要： | 本文对粘性不可压缩Navier-Stokes方程提出了一种等阶稳定化亏量校正有限元法.将通常的压力投影稳定化方法与亏量校正思想相结合,建立了一种稳定的有限元格式,绕开了inf-sup条件的限制,并且克服了当粘性系数很小时造成的不稳定性.对速度/压力采用等阶多项式空间,证明了解的存在唯一性,给出了误差估计.误差估计的结果表明,每校正一步误差的精度提高一阶. |
| 关 键 词： | Navier-Stokes方程 亏量校正 压力投影 粘性系数 |
| 收稿时间： | 2008-05-12 |
A STABILIZED DEFECT CORRECTION METHODS BASED ON EQUAL-ORDER ELEMENTS FOR THE STATIONARY NAVIER-STOKES EQUATIONS |
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| Qin Yanmei,Feng Minfu,Yin Lei.A STABILIZED DEFECT CORRECTION METHODS BASED ON EQUAL-ORDER ELEMENTS FOR THE STATIONARY NAVIER-STOKES EQUATIONS[J].Mathematica Numerica Sinica,2010,32(1):1-14. | |
| Authors: | Qin Yanmei Feng Minfu Yin Lei |
| Institution: | 1. Key Laboratory of Numberical Simulation of Sichuan Province, Neijiang 641112, Sichuan, China; 2. Department of Mathematics, Neijiang Teachers University, Neijiang 641112, Sichuan, China; 3. Department of Mathematics, Sichuan University, Chengdu 610064, China; 4. Department of Mathematics, Sichuan University, Chengdu 610064, China |
| Abstract: | We consider the synthesis of a recent polynomial pressure projection stabilization method with defect correction methods for the incompressible Navier-Stokes equation with a small viscosity coefficient. The combination combines the best features of each. Firstly, it is stable for the equal-order combination of discrete continuous velocity and pressure spaces. Secondly, in the defect step, the artifical viscosity parameter σ is added to the viscosity coefficient as a stability factor. The existence and uniquence are proved for the each step, error estimation is derived for the each step too. The error estimation results show that each step of defect correction method improves the error in the previous step by one power of h. |
| Keywords: | Navier-Stokes equations defect correction pressure projection viscosity coefficient |
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