| 对流占优的Sobolev方程的投影稳定化有限元方法 |
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| 引用本文： | 周琴,潘雪琴,冯民富.对流占优的Sobolev方程的投影稳定化有限元方法[J].计算数学,2014,36(1):99-112. |
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| 作者姓名： | 周琴 潘雪琴 冯民富 |
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| 作者单位： | 四川大学数学学院, 成都 610064 |
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| 基金项目： | 国家自然基金（11271273）资助项目. |
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| 摘 要： | 对于对流占优的Sobolev方程,提出了一种新的投影稳定化有限元方法,建立了半离散和全离散的投影稳定化格式,给出了解的稳定性和收敛性分析.该方法能够有效克服对流占优,与内罚方法相比,投影格式更简单,计算量更小,且得到的C—N格式是无条件稳定的,时间精度达到了二阶.最后,通过实验证明,数值结果与理论结果完全一致.
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| 关 键 词： | Sobolev方程 对流占优 投影方法 离散格式 |
| 收稿时间： | 2013-06-09; |
A PROJECTION-BASED STABILIZED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH CONVECTION-DOMINATED TERM |
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| Zhou Qin,Pan Xueqin,Feng Minfu.A PROJECTION-BASED STABILIZED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH CONVECTION-DOMINATED TERM[J].Mathematica Numerica Sinica,2014,36(1):99-112. |
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| Authors: | Zhou Qin Pan Xueqin Feng Minfu |
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| Institution: | Department of Mathematics, Sichuan University, Chengdu 610064, China |
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| Abstract: | We propose a new projection-based stabilized finite element method for Sobolev equations with convection-dominated term. Basd on the projection idea, semi-discrete and fully discrete approximation scheme are established, the stability and convergence analysis of the solutions are analyzed. The method can effectively handle the influence of dominating convection. Compared with the interior penalty method, projection method is simpler, it's C-N scheme is unconditionally stable, and its time-accuracy is second order. The numerical illustrations agree with the theoretical expectation very well. |
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| Keywords: | Sobolev equation dominating convection projection-based method discrete approximation scheme |
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