Finite element analysis of the singularly perturbed parabolic reaction‐diffusion problems with retarded argument

Abstract

AbstractIn this article, a parameter uniform Galerkin finite element method for solving singularly perturbed parabolic reaction diffusion problems with retarded argument is proposed. The solution of this class of problems exhibits parabolic boundary layers. The domain is discretized with a piecewise uniform mesh (Shishkin mesh) for spatial variable to capture the exponential behavior of the solution in the boundary layer region and backward‐Euler method on a equidistant mesh in the time direction. The method is proved to be unconditional stable and parameter uniform. The method is shown to be accurate of order in maximum norm using Green's function approach. The convergence of the proposed method does not depend on the singular perturbation parameter.