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

Bui Trong Kien, Xiaolong Qin, Ching-Feng Wen, Jen-Chih Yao

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.