稳态自然对流问题的连续内罚有限元方法  

Continuous interior penalty finite element method for steady-state natural convection problems

作　　者：潘雪琴[1] 周琴[1] 冯民富[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2014年第6期1099-1107,共9页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11271273)

摘　　要：本文对于稳态自然对流问题建立了一种内罚有限元格式.该方法通过在通常的混合Galerkin形式中添加能够对速度、压力和温度的梯度跳跃加以L2-控制的稳定项有效地解决了对流占优和速度、压力混合元空间因要求满足LBB条件而造成的解的不稳定性.最后,本文得到了速度、压力、温度的最优先验误差估计.In this paper, we proposed a continuous interior penalty finite element method for solving the steady-state natural convection problems. We added a stabilization term for giving L^2 -control of the jump of the gradient of the velocity, temperature and pressure over element faces to the standard Galer- kin formulation. The method can effectively solve instabilities due to the influence of dominating convec- tion and the requirement of LBB condition for the mixed finite element spaces. At last, finite element er- ror analysis of the problem is investigated and optimal error estimates for the velocity, temperature and pressure are established.

关 键 词：连续内罚方法 误差分析 自然对流问题 

分 类 号：O241.82[理学—计算数学]