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The Schwarz algorithm for a class of elliptic quasi-variational inequalities with nonlinear source terms is studied in this work. The authors prove a new error estimate in uniform norm, making use of a stability property of the discrete solution. The domain is split into two sub-domains with overlapping non-matching grids. This approach combines the geometrical convergence of solutions and the uniform convergence of variational inequalities.

A new error estimate on uniform norm of Schwarz algorithm for elliptic quasi-variational inequalities with nonlinear source terms