对流占优的Sobolev方程的投影稳定化有限元方法  

A PROJECTION-BASED STABILIZED FINITE ELEMENT METHOD FOR SOBOLEV EQUATIONS WITH CONVECTION-DOMINATED TERM

作　　者：周琴[1] 潘雪琴[1] 冯民富[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《计算数学》2014年第1期99-112,共14页Mathematica Numerica Sinica

基　　金：国家自然基金(11271273)资助项目

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.We propose a new projection-based stabilized finite element method for Sobolev equa- tions 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 con- vection. 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 thonrotionl ~ e~ 11

关 键 词：SOBOLEV方程 对流占优 投影方法 离散格式 

分 类 号：O241.82[理学—计算数学]