Energy-conserved splitting spectral methods for two dimensional Maxwell’s equations

In this paper, the energy-conserved splitting Legendre Galerkin method and energy-conserved splitting Legendre collocation method for Maxwell’s equations in two dimensions are proposed. The schemes are energy-conserved, unconditionally stable, and can be implemented efficiently. The both methods are of second-order convergence in time. The high order error estimates in space for the two methods are also obtained. For the EC-S-LC method, an identity of the discrete divergence of electric fields is also obtained. Numerical examples are provided to confirm the theoretical analysis.