Numerical Study of Nonlinear Reaction-Diffusion Equation in CatalyticPellet Model Using Finite Element Method

This study explores numerical solutions to nonlinear reaction-diffusion equations, with a focus on modeling concentration profiles in catalytic pellets, crucial for many chemical engineering applications. The problem is discretised and investigated in both the temporal and spatial domains using finite element method. A weak formulation is developed, and the existence and uniqueness of the finite element method solution are established. Stability and convergence of the numerical schemes are rigorously analyzed, and Crank–Nicolson-based discretization is implemented for enhanced accuracy. Numerical results illustrate the effectiveness of finite element method and finite difference method, with close agreement between the methods. This comparison highlights finite element method’s potential advantages in catalytic process modeling, showcasing its effectiveness in solving nonlinear reaction-diffusion PDEs