对流扩散方程的稳定化流线扩散法最小二乘非协调有限元分析  

The Stabilized Streamline Diffusion Least-Squares Nonconforming Mixed Finite Element Analysics for Stationary Convection-Diffusion Problems

作　　者：于志云[1] 石东伟[2] 石东洋[3] 

机构地区：[1]中原工学院理学院,河南郑州450007 [2]河南科技学院数学系,河南新乡453003 [3]郑州大学数学系,河南郑州450001

出　　处：《数学的实践与认识》2012年第15期228-233,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10671184;10971203);高等学校博士学科点专项科研基金(20094101110006);河南省基础与前沿技术研究计划项目(122300410208)

摘　　要：将最小二乘法和稳定化的流线扩散法相结合,研究了对流扩散方程的非协调有限元格式,用矩形EQ_1^(rot)元和零阶R-T元分别来逼近位移和应力,利用单元本身的特殊性质,证明了离散格式解的存在惟一性,得到了位移H^1-模和应力H(div)-模的最优误差估计.In this paper, combining with the least square method and stabilization streamline diffusion method, the nonconforming mixed finite element scheme is analyzed for convection- diffusion problems. The rectangular EQ1^rot element and zero order R-T element are used to approximate the displacement and the stress, respectively. By use of the special properties of the elements, the existence and uniqueness of the approximate solutions are proved. The optimal order error estimates for the displacement in broken H^1-norm and the stress in H （div）- norm are derived.

关 键 词：对流扩散方程 流线扩散法 非协调元 最小二乘法 最优阶误差估计 

分 类 号：O241.82[理学—计算数学]