Stokes方程基于多尺度函数的稳定化有限元方法  

STABILIZED FINITE ELEMENT METHOD BASED ON MULTISCALE FUNCTIONS FOR THE STOKES EQUATIONS

作　　者：曹济伟[1] 葛志昊[2] 刘鸣放[2] Cao Jiwei Ge Zhihao Liu Mingfang(School of Mathematical Sciences, Nankai University, Tianjin 300071, China School of Mathematics and Statistics ＆ Institute of Applied Mathematics, Henan University, Kaifeng 475004, China)

机构地区：[1]南开大学数学科学学院,天津300071 [2]河南大学数学与统计学院&应用数学所,开封475004

出　　处：《数值计算与计算机应用》2017年第1期68-80,共13页Journal on Numerical Methods and Computer Applications

基　　金：河南省自然科学基金面上项目;河南省基本科研业务费优秀青年基金(yqpy20140039)资助

摘　　要：本文提出一种新的求解Stokes问题的稳定化有限元方法.对于速度场的离散,有限元空间的选取为标准的多项式空间加上多尺度函数.本文证明该方法对于不满足离散的inf-sup条件的最低阶等阶元P_1-P_1元绝对稳定,同时也给出了最优阶误差估计,数值算例验证了理论的正确性.In the paper, a new stabilized finite element method for the Stokes problem is proposed, which is based on the enrichment of the standard polynomial space for the velocity compo- nent with multiscale functions. And the absolute stability of the method for the P1 - P1 triangular element （which do not satisfy the discrete inf-sup condition） is established, so it is an absoultely stable finite element method for the lowest equal order elements. The optimal order convergence analysis is given, and the numerical tests verify the the theoretical results.

关 键 词：稳定化有限元方法 多尺度函数 Stokes方程. 

分 类 号：O241.82[理学—计算数学]