| Abstract: |
| 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-N$\acute{e}$d$\acute{e}$lec element $k\geq 2$ in spatial is established. Based on the truncated error, we present the convergent analysis with the order $O(\Delta t+h^s) $ under the technique of a-prior $L^\infty$ assumption. For the $k=1$, we employ the superconvergence technique to ensure the a-prior $L^\infty$ assumption. In the end, we give some numerical examples to demonstrate our theories. |
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