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We consider a nonlinear second order elliptic boundary value problem (BVP) in a bounded domain with a nonlocal boundary condition. A Dirichlet BC containing an unknown additive constant, accompanied with a nonlocal (integral) Neumann side condition is prescribed at some boundary part Γn . The rest of the boundary is equipped with Dirichlet or nonlinear Robin type BC. The solution is found via linearization. We design a robust and efficient approximation scheme. Error estimates for the linearization algorithm are derived in L 2 (Ω),H 1 (Ω) and L ∞ (Ω) spaces.

Error estimates of an efficient linearization scheme for a nonlinear elliptic problem with a nonlocal boundary condition