An E-based splitting method with a non-matching grid for eddy current equations with discontinuous coefficients

A new decoupled finite element method based on solving a vector and a scalar from the splitting of the electric field is presented to approximate time-dependent eddy current equations with discontinuous coefficients in a three-dimensional polyhedral domain. By introducing a Lagrangian multiplier, this method realizes an optimal control for the interface problem. A non-matching finite element grid on the interface is considered and an optimal energy-norm error estimate in finite time is obtained.