We present a non-overlapping domain decomposition method for the obstacle problem. In this approach, the original problem is reformulated into two subproblems such that the first problem is a variational inequality in subdomain Ω i and the other is a variational equality in the complementary subdomain Ω e , where Ω e and Ω i are multiply-connected, in general. The main challenge is to obtain the global solution through coupling of the two subdomain solutions, which requires the solution of a

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... linear interface problem. This is achieved via a fixed point iteration. This new formulation reduces the computational cost as the variational inequality is solved in a smaller region. The algorithm requires some mild assumption about the location of Ω i , which is the domain containing the region corresponding to the coincidence set. Numerical experiments are included to illustrate the performance of the resulting method. − ∆ z 2 = 0 in Ω e , z 2 = 0 on ∂ Ω \ Γ , z 2 = λ on Γ ,