@Article{NMTMA-8-605,
author = {Tong Kang, Ran Wang, Tao Chen and Huai Zhang},
title = {Fully Discrete $A$-$ϕ$ Finite Element Method for Maxwell's Equations with a Nonlinear Boundary Condition},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2015},
volume = {8},
number = {4},
pages = {605--633},
abstract = {<p style="text-align: justify;">In this paper we present a fully discrete $A$-$ϕ$ finite element method to solve Maxwell&#39;s equations with a nonlinear degenerate boundary condition, which represents a generalization of the classical Silver-Müller condition for a non-perfect conductor. The relationship between the normal components of the electric field $E$ and the magnetic field $H$ obeys a power-law nonlinearity of the type $H&nbsp;× n = n × (|E&nbsp;× n|^{α-1}E × n)$ with $α ∈ (0,1]$. We prove the existence and uniqueness of the solutions of the proposed $A$-$ϕ$ scheme and derive the error estimates. Finally, we present some numerical experiments to verify the theoretical result.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2015.m1413},
url = {http://global-sci.org/intro/article_detail/nmtma/12425.html}
}