一个各向异性插值定理及其在二阶问题混合元中的应用  

AN ANISOTROPIC INTERPOLATETHEOREM AND ITS APPLICATIONSTO THE MIXED FORM OF SECONDORDER ELLIPTIC PROBLEM

作　　者：宋士仓[1] 陈绍春[1] 

机构地区：[1]郑州大学数学系,郑州450052

出　　处：《高等学校计算数学学报》2004年第3期230-240,共11页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金资助项目(10171092);河南省自然科学基金项目.

摘　　要：1引言 设Ω Rn是有界区域,{Jh}是Ω的单元剖分族,J={K1,K2,……,KN},Ω=UK;∈Jh Ki,Ki是单元.对传统的有限元方法,剖分需满足正则性条件或非退化条件,即存在与K∈Jh和Jh无关的常数C,使得hk/pk≤ C,其中hK是K的直径,pk为含于K内最大球的直径.At first this paper presents an interpolate theorem with anisotropic property, which can be applied to estimate the interpolate error based on differ-ent directions. Then a discrete mixed form for the second order elliptic problem is constructed.The gradient vector is approximated by non-full piesewise double quadratic polynomials, the function u by piecewise constants only. The advantage is that this scheme is stili convergent without regularity assumption of subdivision to domain Ω.

关 键 词：二阶 定理 插值 各向异性 

分 类 号：O175[理学—数学]