Approximation of the eigenvalue problem for the time harmonic Maxwell system by continuous Lagrange finite elements
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- by Andrea Bonito and Jean-Luc Guermond PDF
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Abstract:
We propose and analyze an approximation technique for the Maxwell eigenvalue problem using $\mathbf {H}^1$-conforming finite elements. The key idea consists of span style=color:blackconsidering a mixed method/span controlling the divergence of the electric field in a fractional Sobolev space $H^{-\alpha }$ with $\alpha \in (\frac 12,1)$. The method is shown to be convergent and spectrally correct.References
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Additional Information
- Andrea Bonito
- Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843
- MR Author ID: 783728
- Email: bonito@math.tamu.edu
- Jean-Luc Guermond
- Affiliation: Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, Texas 77843. On leave from LIMSI, UPR 3251 CNRS, BP 133, 91403 Orsay cedex, France
- Email: guermond@math.tamu.edu
- Received by editor(s): October 1, 2009
- Received by editor(s) in revised form: July 12, 2010
- Published electronically: February 4, 2011
- Additional Notes: The first author was partially supported by the NSF grant DMS-0914977.
The second author was partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST)
The third author was partially supported by the NSF grant DMS-07138229 - © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 80 (2011), 1887-1910
- MSC (2010): Primary 65N25, 65F15, 35Q61
- DOI: https://doi.org/10.1090/S0025-5718-2011-02464-6
- MathSciNet review: 2813343