New Energy-Conserved Identities and Super-Convergence of the Symmetric EC-S-FDTD Scheme for Maxwell's Equations in 2D (Communications in Computational Physics, 2012)
The symmetric energy-conserved splitting FDTD scheme developed in [1] isa very new and efficient scheme for computing the Maxwell's equations. It is based onsplitting the whole Maxwell's equations and matching the x-direction and y-directionelectric fields associated to the magnetic field symmetrically. In this paper, we makefurther study on the scheme for the 2D Maxwell's equations with the PEC boundarycondition. Two new energy-conserved identities of the symmetric EC-S-FDTD schemein the discrete H1-norm are derived. It is then proved that the scheme is unconditionally stable in the discrete H1-norm. By the new energy-conserved identities, thesuper-convergence of the symmetric EC-S-FDTD scheme is further proved that it isof second order convergence in both time and space steps in the discrete H1-norm.Numerical experiments are carried out and confirm our theoretical results.