Geodesic
An Interior Penalty Method with C 0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity
Bonito, Andrea 1 idref     ; Guermond, Jean-Luc 1 idref     ; Luddens, Francky 2 idref  
1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA.
2 LIMSI, UPR 3251 CNRS, BP 133, 91403 Orsay cedex, France.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 5, pp. 1457-1489 Cet article a éte moissonné depuis la source Numdam

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The present paper proposes and analyzes an interior penalty technique using C 0 -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.

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DOI : 10.1051/m2an/2015086
Classification : 65N25, 65F15, 35Q60
Keywords: Finite elements, Maxwell equations, eigenvalue, discontinuous coefficients, spectral approximation

Bonito, Andrea  1   ; Guermond, Jean-Luc  1   ; Luddens, Francky  2

1 Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA.
2 LIMSI, UPR 3251 CNRS, BP 133, 91403 Orsay cedex, France. 
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     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},
     year = {2016},
     publisher = {EDP-Sciences},
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}
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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

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