In this paper, we explore the numerical analysis of Brusselator-type reaction-diffusion equations on open bounded convex domains \({\mathfrak {R}} \subset {\mathbb {R}}^{d}\) , where \(d \le 3\) , with Robin boundary conditions (RBCs). We introduce two finite element schemes: semi-discrete and fully discrete finite element approximations. We demonstrate the existence and uniqueness of solutions for both semi-discrete and fully discrete finite element approximations. Furthermore, we present the convergence of both semi-discrete and fully discrete approximations to the exact solutions. We explore error bounds between semi-discrete and exact solutions, semi-discrete and fully discrete solutions, as well as fully discrete and exact solutions. Additionally, we illustrate the suitable algorithm for solving the fully discrete finite element approximation for each time step.
