Fully Discrete $A$-$ϕ$ Finite Element Method for Maxwell's Equations with a Nonlinear Boundary Condition
Year: 2015
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 4 : pp. 605–633
Abstract
In this paper we present a fully discrete $A$-$ϕ$ finite element method to solve Maxwell'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 $H × n = n × (|E × n|^{α-1}E × n)$ 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2015.m1413
Numerical Mathematics: Theory, Methods and Applications, Vol. 8 (2015), Iss. 4 : pp. 605–633
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
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