四阶拟线性椭圆方程的有限元误差估计  

Finite Element Error Estimate of Fourth Order Quasilinear Elliptic Equations

作　　者：安荣[1,2] 李开泰[2] 李媛[2] 

机构地区：[1]温州大学数学与信息科学学院,温州325035 [2]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2010年第3期527-533,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571142;10701061;10901122)~~

摘　　要：针对一类四阶拟线性椭圆方程,本文给出了它的协调有限元逼近。当网格参数h足够小时,得到了有限元逼近解与真解之间的误差估计,并且这些误差估计是最优的。最后,通过数值实验验证了理论分析的准确性。证明方法可以类似地应用到某些二阶拟线性椭圆方程的有限元逼近。For a class of fourth order quasilinear elliptic equations, the conforming finite element approximation is presented. If the parameter h of the grid is sufficiently small, the error estimates between the finite element approximation solution and the true solution are obtained. Moreover, these estimates are optimal. Finally, the numerical experiment is given to verify the correctness of the theoretical analysis. The proof method can be extended to the finite element approximation of some second order elliptic equations.

关 键 词：四阶拟线性椭圆方程 有限元逼近 误差估计 

分 类 号：O241.82[理学—计算数学]