In this paper, we investigate a higher-order, parameter uniform numerical scheme for time-dependent singularly perturbed problems with discontinuous reaction coefficient and source term. The solution of these problems exhibits both interior and boundary layers. We employ the semidiscrete non-symmetric interior penalty Galerkin (NIPG) method for spatial discretization on layer adapted Bakhvalov Shishkin and Shishkin meshes. This scheme is analyzed to prove uniform error estimates in both Formula: see text and Formula: see text norms. The fully discrete scheme is formulated using the implicit Formula: see text-scheme on a uniform temporal mesh, establishing parameter uniform error estimates in the discrete Formula: see text norm. Numerical experiments are conducted to validate the theoretical results. Our findings demonstrate the efficacy of the proposed method in handling singularly perturbed problems with discontinuous data.
Yadav et al. (Thu,) studied this question.