Regularization of a Unilateral Obstacle Problem on the Boundary

where f ∈ L2(Ω); it is well known that problems (1.1) and (1.2) admit a unique solution (see [3]). The aim of this paper is to develop a regularization method for solving a nondifferentiable minimization problem that is equivalent to problems (1.1) and (1.2). The idea of the regularization method is to approximate the nondifferentiable term by a sequence of differentiable ones depending on (ε ≥ 0, ε→ 0). We give three forms of regularization for whichwe establish the convergence result and a priori error estimates. Next, by duality method of conjugate functions (see [1]), we provide a posteriori error estimates desired for the numerical computation. And as an application, we develop a regularization method for solving a sequence of penalised problem.