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.

引用

页码：94 / 105

页数：12

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