The Crank–Nicolson mixed finite element method for the improved system of time-domain Maxwell’s equations

Highlights：

• The study process herein is to discrete time and then discrete space variables so as to save the semi-discretized MFE discussion for spatial variables, which is also new attempt.

• The magnetic field strength in the improve system of Maxwell’s equations is independent of the electric intensity such that the MFE subspaces of the magnetic field strength and electric intensity in the FDCNMFE method can avoid the constraint of the Babuska-Brezzi condition and can freely choose, and the MFE solutions reach optimal order error estimates.

• The 2D and 3D FDCNMFE formats have both symmetry and positive definiteness and reach the second-order accuracy in time.

• Both time semi-discretized CN solutions and the FDCNMFE solutions are unconditionally stable and unconditionally convergent. The above these are added Abstract and Remark 3 in revision.