| 定常的热传导-对流问题的Galerkin/Petrov最小二乘混合元方法 |
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| 引用本文： | 罗振东,卢秀敏. 定常的热传导-对流问题的Galerkin/Petrov最小二乘混合元方法[J]. 计算数学, 2003, 25(2): 231-244 |
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| 作者姓名： | 罗振东 卢秀敏 |
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| 作者单位： | 首都师范大学数学系,北京,100037;首都师范大学数学系,北京,100037 |
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| 基金项目： | 国家自然科学基金,北京市教委基金,北京市优秀人才专项经费,北京市自然科学基金资助项目. |
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| 摘 要： | 1.引言 热传导-对流问题是大气动力学中的一个重要的方程,这个方程组也称为强迫耗散的非线性系统方程组,其较Navier-Stokes方程多了一个未知函数温度场,且温度与速度和压力之间存在着复杂的非线性关系.从热动力学可知,任何运动都会产生热量即有温度,而且温度与速度和压力之间必定互相转化,因此对该非线性系统的研究更具有实际意义.[1]先对
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| 关 键 词： | 热传导-对流问题 混合元方法 Galerkin/Petrov最小二乘法 |
| 修稿时间： | 2001-12-26 |
A LEAST SQUARES GALERKIN/PETROV MIXED FINITE ELEMENT METHOD FOR THE STATIONARY CONDUCTION-CONVECTION PROBLEMS |
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| Luo Zhendong Lu Xiumin. A LEAST SQUARES GALERKIN/PETROV MIXED FINITE ELEMENT METHOD FOR THE STATIONARY CONDUCTION-CONVECTION PROBLEMS[J]. Mathematica Numerica Sinica, 2003, 25(2): 231-244 |
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| Authors: | Luo Zhendong Lu Xiumin |
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| Affiliation: | Luo Zhendong Lu Xiumin (Department of Mathematics, Captial Normal University, Beijing, 100037) |
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| Abstract: | In this paper, a Galerkin/Petrov-least squares mixed finite element method for the stationary conduction-convection problems is presented and analyzed. The method is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. The existence, uniqueness and convergence (at optimal rate) of the discrete solution is proved in the case of sufficient viscosity (or small data). |
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| Keywords: | conduction-convection problems mixed finite element method Galerkin/Petrov-least squares-type |
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