Finite element method for a nonlinear parabolic integro-differential equation in higher spatial dimensions

In this paper, we extend and analyze the Galerkin finite element method for the spatial discretization (Jangveladze et al., 2011) to the higher spatial dimensions and develop a numerical algorithm based on θ scheme for the time discretization for solving a parabolic integro-differential equation which arises in the magnetic field penetration process. A-priori bounds are derived for the exact solution. The semi discrete and fully discrete error estimates are derived in L∞(L2(Ω)) and L2(H1(Ω)) norms using energy arguments. Further, we present a numerical experiment which supports the theoretical results.