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.

中文翻译：

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自反Banach空间中变分不等式的Galerkin方法和正则化。

本文研究了Berzis意义上的Galerkin方法的收敛性和带有伪单调算子的变分不等式的正则化。即，我们证明了在一定条件下，Galerkin方程的解和正规化的变分不等式强烈收敛于自反Banach空间中原始变分不等式的解。给出了障碍问题的应用。