Abstract
In this paper, we introduce numerical methods for singularly perturbed convection-diffusion problems with a turning point. As a result of the turning point, the problem typically exhibits exponential-type boundary layers or a cusp-type interior layer. We develop non-symmetric discontinuous Galerkin finite element method with interior penalties (NIPG) for both the cases. Usual Shishkin mesh is invoked for the problem with boundary layers whereas generalized Shishkin type mesh is used to tackle the interior layer of cusp-type. The uniform error estimates are obtained for both the problems in L2-norm and DG-norm. Numerical experiments are conducted to confirm the theoretical estimations.
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