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Fully discrete finite element method for Maxwell's equations with nonlinear conductivity

Stephane Durand UGent and Marian Slodicka UGent (2011) IMA JOURNAL OF NUMERICAL ANALYSIS. 31(4). p.1713-1733
abstract
In this paper we present a numerical scheme to solve nonlinear Maxwell’s equations based on backward Euler discretization in time and curl-conforming finite elements in space. The nonlinearity is due to a field-dependent conductivity in the form of a power law. The system under study is hyperbolic and due to the nonlinear conductivity it lacks strong estimates of the second time derivative. We are able to prove convergence of our numerical scheme based on boundedness of the second derivative in the dual space. Convergence of the nonlinear term is based on the Minty–Browder technique. We also present the error estimate for the fully discretized problem and support the theory by some numerical experiments.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
POLYHEDRAL DOMAINS, SUPERCONDUCTORS, TIME-DISCRETIZATION SCHEME, CONVERGENCE, MODEL, Maxwell's equations, backward Euler, convergence, edge elements, error estimates
journal title
IMA JOURNAL OF NUMERICAL ANALYSIS
IMA J. Numer. Anal.
volume
31
issue
4
pages
1713 - 1733
Web of Science type
Article
Web of Science id
000295987700018
JCR category
MATHEMATICS, APPLIED
JCR impact factor
1.481 (2011)
JCR rank
29/245 (2011)
JCR quartile
1 (2011)
ISSN
0272-4979
DOI
10.1093/imanum/drr007
project
01D28807
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1218404
handle
http://hdl.handle.net/1854/LU-1218404
date created
2011-05-05 17:10:24
date last changed
2012-05-02 15:32:53
@article{1218404,
  abstract     = {In this paper we present a numerical scheme to solve nonlinear Maxwell{\textquoteright}s equations based on backward Euler discretization in time and curl-conforming finite elements in space. The nonlinearity is due to a field-dependent conductivity in the form of a power law. The system under study is hyperbolic and due to the nonlinear conductivity it lacks strong estimates of the second time derivative. We are able to prove convergence of our numerical scheme based on boundedness of the second derivative in the dual space. Convergence of the nonlinear term is based on the Minty--Browder technique. We also present the error estimate for the fully discretized  problem and support the theory by some numerical experiments.},
  author       = {Durand, Stephane and Slodicka, Marian},
  issn         = {0272-4979},
  journal      = {IMA JOURNAL OF NUMERICAL ANALYSIS},
  keyword      = {POLYHEDRAL DOMAINS,SUPERCONDUCTORS,TIME-DISCRETIZATION SCHEME,CONVERGENCE,MODEL,Maxwell's equations,backward Euler,convergence,edge elements,error estimates},
  language     = {eng},
  number       = {4},
  pages        = {1713--1733},
  title        = {Fully discrete finite element method for Maxwell's equations with nonlinear conductivity},
  url          = {http://dx.doi.org/10.1093/imanum/drr007},
  volume       = {31},
  year         = {2011},
}

Chicago
Durand, Stephane, and Marian Slodicka. 2011. “Fully Discrete Finite Element Method for Maxwell’s Equations with Nonlinear Conductivity.” Ima Journal of Numerical Analysis 31 (4): 1713–1733.
APA
Durand, S., & Slodicka, M. (2011). Fully discrete finite element method for Maxwell’s equations with nonlinear conductivity. IMA JOURNAL OF NUMERICAL ANALYSIS, 31(4), 1713–1733.
Vancouver
1.
Durand S, Slodicka M. Fully discrete finite element method for Maxwell’s equations with nonlinear conductivity. IMA JOURNAL OF NUMERICAL ANALYSIS. 2011;31(4):1713–33.
MLA
Durand, Stephane, and Marian Slodicka. “Fully Discrete Finite Element Method for Maxwell’s Equations with Nonlinear Conductivity.” IMA JOURNAL OF NUMERICAL ANALYSIS 31.4 (2011): 1713–1733. Print.