Fully discrete finite element scheme for Maxwell's equations with non-linear boundary condition
type: Item
instance of: scholarly article
title: Fully discrete finite element scheme for Maxwell's equations with non-linear boundary condition
zbMATH Open document ID: 1211.78030
author: S. Durand
author: M. Slodička
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-01-12T00:00:00Z
review text: A study is done of a full Maxwell's system accompanied with a non-linear 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 electric \(E\) and magnetic \(H\) field obeys the following power law \(\nu \times H=\nu \times (|E\times \nu |^{\alpha - 1}E\times \nu )\) for some \(\alpha \in (0,1]\). The existence and uniqueness of a weak solution are established in a suitable function spaces under the minimal regularity assumptions on the boundary \(\Gamma \) and the initial data \(E_{0}\) and \(H_{0}\). A non-linear time discrete approximation scheme is designed and convergence of the approximations to a weak solution is proved. The error estimates are derived for the time discretization. As a next step the fully discrete problem is studied using curl-conforming edge elements and the corresponding error estimates are derived. Finally some numerical experiments are presented.
reviewed by: Nina Shokina
Mathematics Subject Classification ID: 78M10
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 5835293
zbMATH Keywords: Maxwell's equations
zbMATH Keywords: nonlinear Silver-Müller boundary condition
zbMATH Keywords: time discretization
zbMATH Keywords: convergence
zbMATH Keywords: conforming finite elements
zbMATH Keywords: error estimates
describes a project that uses: GetDP
describes a project that uses: Gmsh
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.09.016
OpenAlex ID: W2038325278
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DOI: 10.1016/J.JMAA.2010.09.016
description: scientific article; zbMATH DE number 5835293