Solvability of wave propagation with Debye polarization in nonlinear dielectric materials and its finite element methods approximation

摘要

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-Nedelec element k >= 2 in spatial. Based on the truncated error, we present the convergent analysis with the order O (Delta t + h(s)) under an a-prior L-infinity assumption of numerical solutions. For k = 1, we employ the superconvergence technique to ensure the a-prior L-infinity assumption. In the end, we give some numerical examples to demonstrate our theories. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.