Finite Element Approximation of Singularly Perturbed Parabolic Problems with Discontinuous Reaction Coefficient and Source Function

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.