热传导对流问题的自适应最小二乘Galerkin/Petrov混合有限元法  

Adaptive Mixed Least Squares Galerkin/Petrov Finite Element Method for the Stationary Conduction Convection Problems

作　　者：张运章[1,2] 侯延仁[1] 魏红波[1] 

机构地区：[1]西安交通大学理学院,西安710049 [2]河南科技大学数学与统计学院,河南洛阳471003

出　　处：《应用数学和力学》2011年第10期1182-1198,共17页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1087115611171269)

摘　　要：对热传导对流问题提出了自适应Galerkin/Petrov最小二乘混合有限元法.该算法对任何速度和压力有限元空间的组合是相容和稳定的(不需要满足Babuka-Brezzi稳定性条件).利用Verfürth的一般理论,得到了热传导对流问题的残量型的后验误差估计.最后通过几个数值算例验证了方法的有效性.An adaptive mixed least squares Galerkin/Petrov finite element method was devel- oped for the stationary conduction convection problems. The mixed least squares Galerkin/ Petrov finite element method was consistent and stable for any combination of discrete velocity and pressure spaces （without requiring a Babu^ka-Brezzi stability condition）. Using the general theory of Verftirth, the a posteriori error estimates of residual type are derived for the prob- lems. Finally, some numerical tests are presented to illustrate the method＇ s efficiency.

关 键 词：热传导对流问题 后验误差分析 混合有限元 自适应有限元 最小二乘Galerkin/Petrov法 

分 类 号：O175[理学—数学] O24[理学—基础数学]