New energy identities and super convergence analysis of the energy conserved splitting FDTD methods for 3D Maxwell's equations.

The energy-conserved splitting finite-difference time-domain (EC-S-FDTD) method has recently been proposed to solve the Maxwell equations with second order accuracy while numerically keep the L2 energy conservation laws of the equations. In this paper, the EC-S-FDTD scheme for the 3D Maxwell equations is proved to be energy-conserved and unconditionally stable in the discrete H1 norm. The EC-S-FDTD scheme is of second-order accuracy both in time step and spatial steps, which suggests the super-convergence of this scheme in the discrete H1 norm. And the divergence of the electric field of the EC-S-FDTD scheme in the discrete L2 norm is second-order accurate. Numerical experiments confirm our theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]