A Posteriori Error Analysis for Elliptic Variational Inequalities based on Duality Theory
A Posteriori Error Analysis for Elliptic Variational Inequalities based on Duality Theory
复制标题
基于对偶理论的椭圆变分不等式的后验误差分析
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
HOU Yu-shuang
中科院分区：
文献类型：
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作者：
HeLi-min;WANG Juan;HOU Yu-shuang
本文利用椭圆型变分不等式的对偶理论，对正则化方法进行了较为完整的后验误差分析。本文所考虑的模型问题分别是摩擦接触问题和障碍物问题。选择不同的有界算子形式和函数形式，利用求解不可微极小问题的正则化方法，对它们进行对偶形成，并给出一个H1范数的后验误差估计。利用凸分析中的对偶理论，建立了一般框架下障碍问题的残差型后验误差估计。同时，我们对对偶变量进行了特殊的选择，从而得到了模型问题的基于残差的误差估计及其效率。数值解的后验误差估计是开发有效的自适应算法的基础，而建模误差的后验估计对于分析问题数据中的不确定性对解的影响是有用的。
In this paper, we provide a relatively complete a posteriori error analysis for the regularization method via duality theory for elliptic variational inequalities. The model problems considered in the paper are afriction contact problem and an obstacle problem,respectively. Choosing different bounded operator formand a functional form, we perform their dual formations and givean H1-norm a posteriori error estimation based on the regularization method which is usually used in solving non-differentiable minimization problems. A posteriori error estimates, with residual type for an obstacle problem in the general framework, is established by using duality theory in convex analysis. At the same time,we make a particular choice of the dual variable that leads to a residual-based error estimate of the model problem and its efficiency. A posteriori error estimates for numerical solutions are the basis for developing efficient adaptive algorithms, where as a posteriori estimates for modeling errors are useful for analying the effects of uncertainties in problem data on the solution.