The Galerkin Method and Regularization for Variational Inequalities in Reflexive Banach Spaces

被引：0
作者：
Bui Trong Kien
Xiaolong Qin
Ching-Feng Wen
Jen-Chih Yao
机构：
[1] Quang Trung University,Faculty of Computer Science and Information Technology
[2] Yibin University,Department of Mathematics
[3] Kaohsiung Medical University,Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
[4] Kaohsiung Medical University Hospital,Department of Medical Research
[5] Center for General Education,Department of Applied Mathematics
[6] China Medical University,undefined
[7] National Sun Yat-sen University,undefined
来源：
Journal of Optimization Theory and Applications | 2021年 / 189卷
关键词：
Variational inequality; The Galerkin method; The Galerkin equation; Strong convergence; Monotone operator; Pseudomonotone operator; 47J20; 49J40; 49J53; 90C33;
D O I：
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中图分类号：
学科分类号：
摘要：
This paper studies the convergence of the Galerkin method and regularization for variational inequalities with pseudomonotone operators in the sense of Brézis. Namely, we prove that under certain conditions, the solutions of the Galerkin equations and regularized variational inequalities converge strongly to a solution of the original variational inequality in reflexive Banach spaces. An application for obstacle problems is given.
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页码：578 / 596
页数：18
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