A streamline-diffusion FEM for singularly perturbed degenerate parabolic problem with large delay argument

This article considers a class of singularly perturbed degenerate parabolic problem of convection–diffusion type with large space delay argument. When the convection term dominates over the diffusion term, the solution displays strong boundary layers, while the presence of a delay argument produces a weak interior layer. An implicit finite-difference scheme based on a weighted θ-method is applied for time discretization on an equidistant mesh, and streamline-diffusion finite element method (SDFEM) is used for space discretization on layer-adapted generalized Shishkin mesh. In this study, we have addressed the challenges arising due to the presence of delay argument and degenerate coefficient. The parameter uniform convergence of the proposed method is obtained for the considered class of problems in the maximum norm. Several test problems are considered for the numerical validation and to demonstrate the efficiency of the proposed numerical scheme. Additionally, the solution plots are provided to better illustrate the effect of the delay term.