椭圆问题在三角网格剖分下的扩展混合体积元方法  

Expanded Mixed Element Method of Elliptic Problem under Triangular Grids

作　　者：姜子文[1] 张强[1] 

机构地区：[1]山东师范大学数学科学学院,济南250014

出　　处：《科学技术与工程》2007年第6期943-947,954,共6页Science Technology and Engineering

基　　金：国家自然科学基金(10271068);山东省中青年科学家科研奖励基金项目(2004BS01009);天元基金(A0324647);山东省自然科学基金(Y2002A01)资助

摘　　要：针对一类带有非对角扩散变张量系数的广义自共轭椭圆问题导出的偏微分系统,给出了椭圆问题在三角剖分下的扩展混合体积元方法。该方法在三角单元上采用了最低次的R-T扩展混合元空间,得到近似压力、近似速度以及近似通量的拟最优误差估计。An expanded mixed cobolume method for a system of firstorder PDEs resulting from the mixed formulation of a general self-adjoint elliptic problem with a full diffusion tensor on triangular grids is presented. The lowest order R - T mixed element space on triangular grids is used. Optimal rate of convergence for approximate pressure, as well as for approximate velocity and it＇s flux（ the coefficient times the gradient） is obtained for this formulation.

关 键 词：椭圆问题 混合体积元方法 扩展混合元方法 最优误差估计 

分 类 号：O175.25[理学—数学]