Convergence of a discrete scheme in a regularization method for the quasi-steady Maxwell system in a nonhomogeneous conducting medium

Convergence of the discrete solution to the solution of a regularized system of the Maxwell equations written in terms of a vector magnetic potential with a special calibration of medium's conduction is considered. The problem is discretized by a Nedelec vector finite element method in space and by an implicit Euler scheme in time. An optimal theoretical energy estimate of the approximate solution error in 3D Lipschitz polyhedral domains is obtained. © 2011 Pleiades Publishing, Ltd.