p-Laplace方程的后验误差估计  

A POSTERIORI FEM ERROR CONTROL FOR THE p-LAPLACE EQUATION

作　　者：梁雨欣 刘东杰[1] Liang Yuxin;Liu Dongjie(Department of Mathematics,College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院数学系,上海200444

出　　处：《数值计算与计算机应用》2023年第3期313-326,共14页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11571226)资助。

摘　　要：本文在新的距离的框架下考虑p-Laplace方程的自适应有限元方法.在文献[13]中作者考虑了2≤p<∞的情况,给出了具有上界的后验误差估计本文在此基础上发展了1<p<∞时具有上界和下界的后验误差估计.数值实验验证了理论分析的结果.The adaptive finite element method(AFEM)for the P-Laplace equation in a newly defned distance was studied by D.JLiu and Z.R.Chen[13]for the special case 2≤p<∞,where a posteriori error estimators with upper bound were obtained for conforming and nonconforming FEM.This paper focuses on the case when 1<p<∞,and the a posteriori error estimators with both upper and lower bounds are provided.The numerical investigation for benchmark problem provides the accuracy and robustness of the proposed a posteriori errorestimators.

关 键 词：P-LAPLACE方程 自适应有限元方法 后验误差估计 

分 类 号：O241.82[理学—计算数学]