A new a priori estimation for singularly perturbed problems with discontinuous data.

The main aim of this article is to present an a priori estimate of an exponential layer and thereby a new mesh (G-mesh) for a class of singularly perturbed problems with discontinuous data. We have also proved that the standard upwind scheme on the proposed mesh is parameter uniformly convergent and is of almost first order. To demonstrate the efficiency of the proposed mesh we carried out a few numerical experiments comparing the performance of the proposed G-mesh with other standard meshes available in the literature. [ABSTRACT FROM AUTHOR]