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Application of the div-curl lemma for Maxwell's equations with a non-linear conductivity

Stephane Durand UGent (2011) JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. 8(2). p.257-267
abstract
In this paper, we study a non-linear hyperbolic system, occuring in the study of electromagnetic fields in the presence of superconductors. The constitutive relation between current density and the electric field is then highly non-linear. Based on a stability estimate in the dual space, we are able to prove the convergence of backward Euler's method toward the unique solution of the problem. This requires a compensated compactness argument (div-curl lemma) and the Minty-Browder procedure to pull weak convergence through a monotone non-linearity. Finally, we present the corresponding error estimates.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Backward Euler, BOUNDARY-CONDITION, II SUPERCONDUCTORS, error estimates, Maxwell equations, div-curl lemma
journal title
JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS
J. Hyberbolic Differ. Equ.
volume
8
issue
2
pages
257 - 267
Web of Science type
Article
Web of Science id
000292374900003
JCR category
MATHEMATICS, APPLIED
JCR impact factor
0.796 (2011)
JCR rank
105/245 (2011)
JCR quartile
2 (2011)
ISSN
0219-8916
DOI
10.1142/S0219891611002408
project
BOF01D28807
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1221020
handle
http://hdl.handle.net/1854/LU-1221020
date created
2011-05-10 20:21:56
date last changed
2012-05-02 15:34:19
@article{1221020,
  abstract     = {In this paper, we study a non-linear hyperbolic system, occuring in the study of electromagnetic fields in the presence of superconductors. The constitutive relation between current density and the electric field is then highly non-linear. Based on a stability estimate in the dual space, we are able to prove the convergence of backward Euler's method toward the unique solution of the problem. This requires a compensated compactness argument (div-curl lemma) and the Minty-Browder procedure to pull weak convergence through a monotone non-linearity. Finally, we present the corresponding error estimates.},
  author       = {Durand, Stephane},
  issn         = {0219-8916},
  journal      = {JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS},
  keyword      = {Backward Euler,BOUNDARY-CONDITION,II SUPERCONDUCTORS,error estimates,Maxwell equations,div-curl lemma},
  language     = {eng},
  number       = {2},
  pages        = {257--267},
  title        = {Application of the div-curl lemma for Maxwell's equations with a non-linear conductivity},
  url          = {http://dx.doi.org/10.1142/S0219891611002408},
  volume       = {8},
  year         = {2011},
}

Chicago
Durand, Stephane. 2011. “Application of the Div-curl Lemma for Maxwell’s Equations with a Non-linear Conductivity.” Journal of Hyperbolic Differential Equations 8 (2): 257–267.
APA
Durand, S. (2011). Application of the div-curl lemma for Maxwell’s equations with a non-linear conductivity. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 8(2), 257–267.
Vancouver
1.
Durand S. Application of the div-curl lemma for Maxwell’s equations with a non-linear conductivity. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS. 2011;8(2):257–67.
MLA
Durand, Stephane. “Application of the Div-curl Lemma for Maxwell’s Equations with a Non-linear Conductivity.” JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS 8.2 (2011): 257–267. Print.