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In this paper, we study a nonmatching grid finite element approximation of a class of elliptic variational inequalities with nonlinear source terms in the context of the Schwarz alternating domain decomposition. We show that the approximation converges optimally in the maximum norm, on each subdomain, making use of a Lipschitz continuous dependence with respect to both the boundary condition and the source term. MSC: 65K15; 65N30; 65N15doi:10.1186/s13660-016-1110-4 fatcat:4q3oetcaubclvjztzl7lg3e7fq