Asymptotic streamline diffusion finite element method for singularly perturbed convection–diffusion differential difference equations

Abstract

In this article, we presented an asymptotic streamline diffusion finite element method (SDFEM) for singularly perturbed convection–diffusion‐type differential difference equations. Using the asymptotic expansion approximation, the differential difference equations are converted into nondelay differential equations. A SDFEM is applied to the modified equation. Further, we proved that the method gives an almost second‐order convergence in maximum norm, in L2‐norm whereas first‐order convergence in H1‐norm. Numerical results are presented to validate the theoretical results.