Crank-Nicolson Fully Discrete H 1 -Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model

Abstract

We consider a fully discrete $H^1$-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 $L^2$ and $H^1$ norm and its gradient function in $L^2$ norm are presented. A numerical example is given to verify the theoretical results.