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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| Published in | ESAIM. Mathematical modelling and numerical analysis Vol. 50; no. 5; pp. 1457 - 1489 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Les Ulis
EDP Sciences
01.09.2016
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| Subjects | |
| Online Access | Get full text |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Bonito, Andrea Luddens, Francky Guermond, Jean-Luc |
| Author_xml | – sequence: 1 givenname: Andrea surname: Bonito fullname: Bonito, Andrea organization: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA – sequence: 2 givenname: Jean-Luc surname: Guermond fullname: Guermond, Jean-Luc organization: Department of Mathematics, Texas A&M University, College Station, TX 77843-3368, USA – sequence: 3 givenname: Francky surname: Luddens fullname: Luddens, Francky organization: LIMSI, UPR 3251 CNRS, BP 133, 91403 Orsay cedex, France |
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| ContentType | Journal Article |
| Copyright | 2016. Notwithstanding the ProQuest Terms and conditions, you may use this content in accordance with the associated terms available at https://www.esaim-m2an.org/articles/m2an/abs/2016/05/m2an140083/m2an140083.html . |
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| Notes | 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 |
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| Snippet | The present paper proposes and analyzes an interior penalty technique using C0-finite elements to solve the Maxwell equations in domains with heterogeneous... |
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| SubjectTerms | 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 |
| Title | An Interior Penalty Method with C0 Finite Elements for the Approximation of the Maxwell Equations in Heterogeneous Media: Convergence Analysis with Minimal Regularity |
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