Finite element approximations of a nonlinear diffusion model with memory

The article of record as published may be located at http://dx.doi.org/10.1007/s11075-012-9658-7The convergence of a finite element scheme approximating a nonlinear system of integro-differential equations is proven. This system arises in mathematical modeling of the process of a magnetic field penetrating into a substance. Properties of existence, uniqueness and asymptotic behavior of the solutions are briefly described. The decay of the numerical solution is compared with both the theoretical and finite difference results