Crank-Nicolson-Galerkin finite element scheme for nonlocal coupled parabolic problem using the Newton's method

摘要

In this article, a finite element scheme based on the Newton's method is proposed to approximate the solution of a nonlocal coupled system of parabolic problem. The Crank-Nicolson method is used for time discretization. Well-posedness of the problem is discussed at continuous and discrete levels. We derive a priori error estimates for both semidiscrete and fully discrete formulations. Results based on usual finite element method are provided to confirm the theoretical estimates.