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Adaptive finite element method for nonmonotone quasi-linear elliptic problems
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-04-19 , DOI: 10.1016/j.camwa.2021.03.034 Liming Guo , Chunjia Bi
中文翻译:
非单调拟线性椭圆问题的自适应有限元方法
更新日期:2021-04-19
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2021-04-19 , DOI: 10.1016/j.camwa.2021.03.034 Liming Guo , Chunjia Bi
In this paper, we study the simplest and the most standard adaptive finite element method for the second-order nonmonotone quasi-linear elliptic problems with the exact solution . The adaptive algorithm is based on the residual-based a posteriori error estimators and Dörfler’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.
中文翻译:
非单调拟线性椭圆问题的自适应有限元方法
在本文中,我们研究了最简单,最标准的自适应二阶非单调拟线性椭圆问题的自适应有限元方法,并给出了精确解 。自适应算法基于基于残差的后验误差估计器和Dörfler的标记策略。当初始网格足够精细时,我们证明了自适应有限元方法的收敛性和拟最优性。提供数值实验来说明我们的发现。