Comparative study of slow and fast diffusion processes via quadratic and cubic B-spline Galerkin method

Abstract

This study proposes a numerical scheme employing quadratic and cubic B-spline finite element methods (FEM) for solving nonlinear diffusion equations. For time discretization, a finite difference method is applied, while spatial approximation is performed using the B-spline-based Galerkin approach. The method's accuracy is demonstrated through three numerical examples, evaluated using the E2 and E∞ error norms. Stability is analyzed via the von Neumann method and confirmed using a matrix-based approach. The scheme is straightforward to implement and offers an efficient and reliable framework for the numerical solution of nonlinear diffusion problems.

Keywords

• B-spline
• Slow and fast diffusion
• Finite element method
• Stability analysis
• Finite difference