Crank-Nicolson Fully Discrete H1-Galerkin Mixed Finite Element Approximation of One Nonlinear Integrodifferential Model

Abstract EN

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.