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| 求解线性Sobolev方程的分裂型最小二乘混合元方法 | |
| 引用本文： | 高夫征,芮洪兴. 求解线性Sobolev方程的分裂型最小二乘混合元方法[J]. 计算数学, 2008, 30(3): 269-282 |
| 作者姓名： | 高夫征 芮洪兴 |
| 作者单位： | 山东大学数学与系统科学学院,济南,250100;山东大学数学与系统科学学院,济南,250100 |
| 基金项目： | 山东大学数学与系统科学学院专项青年基金，国家自然科学基金，高等学校博士学科点专项科研项目 |
| 摘 要： | 本文通过引入适当的最小二乘极小化泛函,对一类线性Sobolev方程提出了两种分裂型最小二乘混合元格式,格式最大优点在于将耦合的方程组系统分裂成两个独立的子系统,进而极大降低了原问题求解的难度和规模,理论分析表明格式对原未知量及新引入的未知通量分别具有最优阶L2(Ω)模误差估计和次优阶H(div;Ω)模误差估计.数值试验很好的验证了这一点. |
| 关 键 词： | Sobolev方程 最小二乘法 混合有限元 误差估计 数值试验 |
TWO SPLITTING LEAST-SQUARES MIXED ELEMENT METHODS FOR LINEAR SOBOLEV EQUATIONS |
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| Gao Fuzheng,Rui Hongxing. TWO SPLITTING LEAST-SQUARES MIXED ELEMENT METHODS FOR LINEAR SOBOLEV EQUATIONS[J]. Mathematica Numerica Sinica, 2008, 30(3): 269-282 | |
| Authors: | Gao Fuzheng Rui Hongxing |
| Affiliation: | School of Mathematics and System Science, Shandong University, Jinan 250100, China |
| Abstract: | In this paper, two splitting least-squares mixed element methods are proposed to simulate a class of linear Sobolev equations. The methods' advantage is that the coupled system can be split into two independent sub-systems. Theoerical analysis shows that the methods yield the approximate solutions for the primal unknown with optimal accuracy in $L^2(Omega)$ norm and for the unknown flux introdued with sub-optimal accuracy in $H(mbox{div};Omega)$ norm, respectively. Finally, some numerical examples are provided to illustrate the efficiency of the methods. |
| Keywords: | Sobolev equations Least-squares Mixed element Error estimates Numerical examples |
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