单调型非线性椭圆问题的边残量型后验误差估计  

A Posteriori Error Estimates of Edge Residual Type of Finite Element Method for Monotone Nonlinear Elliptic Problems

作　　者：郭利明[1] 黄自萍[1] 王琤[1] 

机构地区：[1]同济大学数学系,上海200092

出　　处：《同济大学学报（自然科学版）》2015年第9期1438-1442,共5页Journal of Tongji University:Natural Science

基　　金：国家自然科学基金(11101311);中德教席基金(0900101021)

摘　　要：针对单调型非线性椭圆问题,研究了线性协调有限元的边残量型后验误差估计.在真解u仅具有H1(Ω)正则性的情况下,证明了边残量在后验误差估计中是占优的,并得到了自适应有限元方法的H1-范数误差可计算的上下界.不计高阶项,边残量可作为线性协调有限元的后验误差估计子.数值算例验证了该边残量型后验误差估计子的有效性.The edge residual-based a posterion error estimates of conforming linear finite element method are studied for the monotone nonlinear elliptic problems. Under the assumption of U∈ H1 （Ω）, we prove that the edge residuals dominate a posteriori error estimates, and obtain the computable global upper and local lower bounds on the error of the adaptive finite element method in H1-norm. Up to higher order terms, edge residuals can be a posteriori error estimators. Numerical examples show the efficiency of the edge residual-based a posteriori error estimators.

关 键 词：后验误差估计 单调型 非线性椭圆问题 边残量 

分 类 号：O241.8[理学—计算数学]