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.
Accepted:
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 VL - 50 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015086/ DO - 10.1051/m2an/2015086 LA - en ID - M2AN_2016__50_5_1457_0 ER -
%0 Journal Article %A Bonito, Andrea %A Guermond, Jean-Luc %A Luddens, Francky %T An Interior Penalty Method with $C^{0}$ Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2016 %P 1457-1489 %V 50 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015086/ %R 10.1051/m2an/2015086 %G en %F M2AN_2016__50_5_1457_0
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 , Volume 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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