The present paper proposes and analyzes an interior penalty technique using -finite elements to solve the Maxwell equations in domains with heterogeneous properties. The convergence analysis for the boundary value problem and the eigenvalue problem is done assuming only minimal regularity in Lipschitz domains. The method is shown to converge for any polynomial degrees and to be spectrally correct.
Accepté le :
DOI : 10.1051/m2an/2015086
Mots-clés : Finite elements, Maxwell equations, eigenvalue, discontinuous coefficients, spectral approximation
@article{M2AN_2016__50_5_1457_0,
author = {Bonito, Andrea and Guermond, Jean-Luc and Luddens, Francky},
title = {An {Interior} {Penalty} {Method} with $C^{0}$ {Finite} {Elements} for the {Approximation} of the {Maxwell} {Equations} in {Heterogeneous} {Media:} {Convergence} {Analysis} with {Minimal} {Regularity}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1457--1489},
publisher = {EDP-Sciences},
volume = {50},
number = {5},
year = {2016},
doi = {10.1051/m2an/2015086},
zbl = {1352.78014},
mrnumber = {3554549},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2015086/}
}
TY - JOUR
AU - Bonito, Andrea
AU - Guermond, Jean-Luc
AU - Luddens, Francky
TI - An Interior Penalty Method with $C^{0}$ Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity
JO - ESAIM: Mathematical Modelling and Numerical Analysis
PY - 2016
SP - 1457
EP - 1489
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PB - EDP-Sciences
UR - http://www.numdam.org/articles/10.1051/m2an/2015086/
DO - 10.1051/m2an/2015086
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Bonito, Andrea; Guermond, Jean-Luc; Luddens, Francky. An Interior Penalty Method with $C^{0}$ Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1457-1489. doi : 10.1051/m2an/2015086. http://www.numdam.org/articles/10.1051/m2an/2015086/
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