An Interior Penalty Method with C0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity

The present paper proposes and analyzes an interior penalty technique using C0-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 Lipsc...

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Bibliographic Details
Published inESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 5; pp. 1457 - 1489
Main Authors Bonito, Andrea, Guermond, Jean-Luc, Luddens, Francky
Format Journal Article
LanguageEnglish
Published Les Ulis EDP Sciences 01.09.2016
Subjects
35Q60
65F15
65N25
Boundary value problems
Convergence
discontinuous coefficients
Domains
eigenvalue
Eigenvalues
Finite elements
Mathematical analysis
Maxwell equations
Maxwell's equations
Polynomials
Regularity
spectral approximation
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Summary:The present paper proposes and analyzes an interior penalty technique using C0-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.
Bibliography:istex:1A02F47971E52C900043F9D85C259CB53B3004B1
bonito@math.tamu.edu; guermond@math.tamu.edu
ark:/67375/80W-SC379C92-W
This material is based upon work supported in part by the National Science Foundation grants DMS-1254618, DMS-1015984. Parts of this work was done during visits of Francky Luddens at Texas A&M. The support of the University Paris-Sud 11 is acknowledged.
PII:S0764583X15000862
publisher-ID:m2an140083
ISSN:0764-583X
1290-3841
DOI:10.1051/m2an/2015086