Finite element approximations of a nonlinear diffusion model with memory
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The 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.
The article of record as published may be located at http://dx.doi.org/10.1007/s11075-012-9658-7