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

Bui Trong Kien (), Xiaolong Qin (), Ching-Feng Wen () and Jen-Chih Yao ()
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Bui Trong Kien: Quang Trung University
Xiaolong Qin: Yibin University
Ching-Feng Wen: Kaohsiung Medical University
Jen-Chih Yao: Center for General Education, China Medical University

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 2, No 10, 578-596

Abstract: Abstract 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.

Keywords: Variational inequality; The Galerkin method; The Galerkin equation; Strong convergence; Monotone operator; Pseudomonotone operator; 47J20; 49J40; 49J53; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01844-9

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