Crank-Nicolson Fully Discrete H1-Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model - Fengxin Chen (Abstract and Applied Analysis)
We consider a fully discrete H1-Galerkin mixed finite element approximation of one nonlinear integrodifferential model which often arises in mathematical modeling of the process of a magnetic field penetrating into a substance. We adopt the Crank-Nicolson discretization for time derivative. Optimal order a priori error estimates for the unknown function in L2 and H1 norm and its gradient function in L2 norm are presented. A numerical example is given to verify the theoretical results.