Numerical solution for a nonlinear obstacle problem

A monotone iterations algorithm combined with the finite difference method is constructed for an obstacle problem with semilinear elliptic partial differential equations of second order. By means of Dirac delta function to improve the computation procedure of the discretization, the finite difference method is still practicable even though the obstacle boundary is irregular. The numerical simulations show that our proposed methods are feasible and effective for the nonlinear obstacle problem.