Adaptive finite element method for nonmonotone quasi-linear elliptic problems

被引：2
|
作者：
Guo, Liming [1 ]
Bi, Chunjia [2 ]
机构：
[1] Xinyang Normal Univ, Coll Math & Stat, Xinyang 464000, Peoples R China
[2] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Peoples R China
来源：
COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2021年 / 93卷
基金：
中国国家自然科学基金;
关键词：
Adaptive finite element method; Convergence; Quasi-optimality; Nonmonotone; Quasi-linear elliptic problems; POSTERIORI ERROR ESTIMATION; OPTIMAL CONVERGENCE RATE; OPTIMALITY; EQUATIONS;
D O I：
10.1016/j.camwa.2021.03.034
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the simplest and the most standard adaptive finite element method for the secondorder nonmonotone quasi-linear elliptic problems with the exact solution u epsilon H-0(1+alpha) (Omega), alpha >= 1/2. The adaptive algorithm is based on the residual-based a posteriori error estimators and Dorfler's marking strategy. We prove the convergence and quasi-optimality of the adaptive finite element method when the initial mesh is sufficiently fine. Numerical experiments are provided to illustrate our findings.
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页码：94 / 105
页数：12
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