Finite Element Methods For Wave Propagation With Debye Polarization In Nonlinear Dielectric Materials

In this paper,we consider the wave propagation with Debye polarization in nonlinear dielectric materials.For this model,the Rother's method is employed to derive the well-posedness of the electric fields and the existence of the polarized fields by monotonicity theorem as well as the boundedness of the two fields are established.Then,decoupled the full-discrete scheme of the Euler in time and Raviart-Thomas-Nedelec element k?2 in spatial is established.Based on the truncated error,we present the convergent analysis with the order O(?t + h~s)under the technique of a-prior L? assumption.For the k= 1,we employ the superconvergence technique to ensure the a-prior L00 assumption.In the end,we give some numerical examples to demonstrate our theories.