A method of discretization for the Lagerström-Cole model equation

A method of discretization for a non linear singularly perturbed boundary value problem is considered. It involves a certain number of steps, one of them including the application of Petrov-Galerkin finite element methods. The resulting scheme is called adjoint method scheme and is in some way related to Niijima's scheme (cf. [11]). It is proved that this discretization provides existence and uniqueness of solution for a problem defined by the Lagerström- Cole model equation. Finally some numerical experiments compare the results obtained when the adjoint method scheme is used, as well as when Niijima's scheme or a direct finite element discretization are applied.