期刊
NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS
卷 5, 期 2, 页码 131-156出版社
GLOBAL SCIENCE PRESS
DOI: 10.4208/nmtma.2012.m1023
关键词
quasilinear elliptic equations; adaptive finite element methods; optimality
资金
- CONICET [PIP 112-200801-02182]
- Universidad Nacional del Litoral [CAI+D PI 062-312]
- Agencia Nacional de Promocion Cientifica y Tecnologica [PICT-2008-0622]
- Universidad Nacional de San Luis (Argentina) [22/F730-FCFMyN]
We prove the quasi-optimal convergence of a standard adaptive finite element method (AFEM) for a class of nonlinear elliptic second-order equations of monotone type. The adaptive algorithm is based on residual-type a posteriori error estimators and Dorfler's strategy is assumed for marking. We first prove a contraction property for a suitable definition of total error, analogous to the one used by Diening and Kreuzer (2008) and equivalent to the total error defined by Cascon et. al. (2008). This contraction implies linear convergence of the discrete solutions to the exact solution in the usual H-1 Sobolev norm. Secondly, we use this contraction to derive the optimal complexity of the AFEM. The results are based on ideas from Diening and Kreuzer and extend the theory from Cascon et. al. to a class of nonlinear problems which stem from strongly monotone and Lipschitz operators.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据