A minimax approach for the study of systems of variational equations and related Galerkin schemes

Abstract

The aim of this work is to analyze the existence of a solution for a quite general variational inequalities system, which includes those appearing in the theory of mixed variational equations, the so-called Babuška–Brezzi theory. It is done by means of a minimax inequality, which also provides us with a estimate of the norm of the solution. Then, we derive a numerical method of the Galerkin type to approximate the solution of such a system. Its stability follows from the mentioned control of the norm of the solution.