An efficient operator splitting weak Galerkin method for singularly perturbed 2D parabolic PDEs

In this paper, we have introduced an operator splitting weak Galerkin finite element method (WG-FEM) for a class of second order singularly perturbed time-dependent convection-diffusion-reaction problem in 2D. The suggested operator splitting approach divides the original model problem into two subproblems each in 1D, then solving each subproblem using WG-FEM in spatial direction eventually reduces the computational difficulty and high storage requirements. Backward Euler scheme is used for temporal derivative. Stability of the fully-discrete scheme has been studied and epsilon\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon $$\end{document}-uniform error estimates have been established. Numerical examples are provided validating our theoretical findings.