Discontinuous Galerkin approach for two parametric convection-diffusion equation with discontinuous source term

In this article, we explore the discontinuous Galerkin finite element method (DGFEM) for two-parametric singularly perturbed convection-diffusion problems with a discontinuous source term. Due to the discontinuity in the source term, the problem typically shows a weak interior layer. Also, the presence of the multiple perturbation parameters in the problem cause boundary layers on both the sides of the boundary. In this work we develop the non-symmetric discontinuous Galerkin finite element method with interior penalties (NIPG) to handle the layer phenomenon. With the use of a typical Shishkin mesh, the domain is discretized and uniform error estimate is obtained. The numerical experiments are conducted to validate the theoretical conclusions.

Keywords:

Convection-diffusion problem , The NIPG methods , Shishkin mesh , Interior layers , Uniform convergence