Abstract
In this paper, we consider the wave propagation with Debye polarization in nonlinear dielectric materials. The Rothe's method is employed to derive the well-posedness of the electric fields and the polarized fields by monotonicity theorem as well as the boundedness of the two fields are established. Then, the decoupled full-discrete scheme is established with the first order approximation in time and Raviart-Thomas-Nédélec element k≥2 in spatial. Based on the truncated error, we present the convergent analysis with the order O(Δt+hs) under an a-prior L∞ assumption of numerical solutions. For k=1, we employ the superconvergence technique to ensure the a-prior L∞ assumption. In the end, we give some numerical examples to demonstrate our theories.
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