NIPG Method on Shishkin Mesh for Singularly Perturbed Convection–Diffusion Problem with Discontinuous Source Term

Abstract

In this paper, we provide numerical approaches for singularly perturbed convection–diffusion problem with a discontinuous source term. As a result of the discontinuity in the source term, the problem highlights an exponential-type boundary layer and a weak interior layer. To handle both the layers at the same time, we design a nonsymmetric discontinuous Galerkin finite element technique with interior penalties (NIPG). The problem is solved using the standard Shishkin mesh. In the DG norm, uniform error estimates are derived for the problem. To verify the theoretical estimates, numerical tests are carried out.