A finite element approach for analysis and computational modelling of coupled reaction diffusion models

Abstract

In this article, we establish the existence and uniqueness of solutions to the coupled reaction–diffusion models using Banach fixed point theorem. The Galerkin finite element method is used for the approximation of solutions, and an a priori error estimate is derived for such approximations. A scheme is proposed by combining the Crank–Nicolson and the predictor–corrector methods for the time discretization. Some numerical examples are considered to illustrate the accuracy and efficiency of the proposed scheme. It is found that the scheme is second‐order convergent. In addition, nonuniform grids are used in some cases to enhance the accuracy of the scheme.