Open Access
Issue |
ESAIM: M2AN
Volume 56, Number 1, January-February 2022
|
|
---|---|---|
Page(s) | 287 - 301 | |
DOI | https://doi.org/10.1051/m2an/2022001 | |
Published online | 10 February 2022 |
- A.B. Andreev and T.D. Todorov, Isoparametric finite-element approximation of a Steklov eigenvalue problem. IMA J. Numer. Anal. 24 (2004) 309–322. [CrossRef] [MathSciNet] [Google Scholar]
- D.N. Arnold, R.S. Falk and R. Winther, Multigrid in H(div) and H(curl). Numer. Math. 85 (2000) 197–217. [CrossRef] [MathSciNet] [Google Scholar]
- I. Babuška and J.E. Osborn, Eigenvalue problems. In: Handbook of Numerical Analysis, edited by P.G. Ciarlet and J.L. Lions. Vol. II. Elseveier Science Publishers B.V., North-Holland (1991). [Google Scholar]
- S. Bergman and M. Schiffer, Kernel Functions and Elliptic Differential Equations in Mathematical Physics. Academic Press (1953). [Google Scholar]
- D. Boffi, Finite element approximation of eigenvalue problems. Acta Numer. 19 (2010) 1–120. [Google Scholar]
- J.H. Bramble and J. Osborn, Approximation of Steklov eigenvalues of non-selfadjoint second order elliptic operators. In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Elsevier (1972) 387–408. [Google Scholar]
- A. Buffa and P. Ciarlet Jr, On traces for functional spaces related to Maxwell’s equations Part I: an integration by parts formula in Lipschitz polyhedra. Math. Methods Appl. Sci. 24 (2001) 9–30. [CrossRef] [MathSciNet] [Google Scholar]
- A. Buffa, M. Costabel and C. Schwab, Boundary element methods for Maxwell’s equations on non-smooth domains. Numer. Math. 92 (2002) 679–710. [CrossRef] [MathSciNet] [Google Scholar]
- A. Buffa, M. Costabel and D. Sheen, On traces for H(curl, Ω) in Lipschitz domains. J. Math. Anal. App. 276 (2002) 845–867. [Google Scholar]
- F. Cakoni, D. Colton, S. Meng and P. Monk, Stekloff eigenvalues in inverse scattering. SIAM J. Appl. Math. 76 (2016) 1737–1763. [Google Scholar]
- J. Camaño, C. Lackner and P. Monk, Electromagnetic Stekloff eigenvalues in inverse scattering. SIAM J. Math. Anal. 49 (2017) 4376–4401. [Google Scholar]
- S. Cogar, D. Colton and P. Monk, Using eigenvalues to detect anomalies in the exterior of a cavity. Inverse Prob. 34 (2018) 085006. [CrossRef] [Google Scholar]
- C. Conca, M. Vanninathan and J. Planchard, Fluids and Periodic Structures. Wiley (1995). [Google Scholar]
- M. Costabel, A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains. Math. Methods Appl. Sci. 12 (1990) 365–368. [Google Scholar]
- B. Gong, J. Sun and X. Wu, Finite element approximation of the modified Maxwell’s Stekloff eigenvalues. SIAM J. Numer. Anal. 59 (2021) 2430–2448. [CrossRef] [MathSciNet] [Google Scholar]
- M. Halla, Electromagnetic steklov eigenvalues: approximation analysis. ESAIM: M2AN 55 (2021) 57–76. [CrossRef] [EDP Sciences] [Google Scholar]
- I. Harris, F. Cakoni and J. Sun, Transmission eigenvalues and non-destructive testing of anisotropic magnetic materials with voids. Inverse Prob. 30 (2014) 035016. [CrossRef] [Google Scholar]
- R. Hiptmair and C. Schwab, Natural boundary element methods for the electric field integral equation on polyhedra. SIAM J. Numer. Anal. 40 (2002) 66–86. [CrossRef] [MathSciNet] [Google Scholar]
- Q. Li, Q. Lin and H. Xie, Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations. App. Math. 58 (2013) 129–151. [CrossRef] [Google Scholar]
- J. Liu, J. Sun and T. Turner, Spectral indicator method for a non-selfadjoint Steklov eigenvalue problem. J. Sci. Comput. 79 (2019) 1814–1831. [Google Scholar]
- P. Monk, Finite Element Methods for Maxwell’s Equations. Oxford University Press (2003). [Google Scholar]
- D. Mora, G. Rivera and R. Rodrguez, A virtual element method for the Steklov eigenvalue problem. Math. Models Methods Appl. Sci. 25 (2015) 1421–1445. [Google Scholar]
- J. Sun and A. Zhou, Finite Element Methods for Eigenvalue Problems. CRC Press, Boca Raton, London, New York (2016). [CrossRef] [Google Scholar]
- H. Xie, A type of multilevel method for the Steklov eigenvalue problem. IMA J. Numer. Anal. 34 (2014) 592–608. [Google Scholar]
- F. Xu, M. Yue, Q. Huang and H. Ma, An asymptotically exact a posteriori error estimator for non-selfadjoint Steklov eigenvalue problem. Appl. Numer. Math. 156 (2020) 210–227. [Google Scholar]
- Y. Yang, Q. Li and S. Li, Nonconforming finite element approximations of the Steklov eigenvalue problem. Appl. Numer. Math. 59 (2009) 2388–2401. [CrossRef] [MathSciNet] [Google Scholar]
- Y. Yang, Y. Zhang and, H. Bi, Non-conforming Crouzeix-Raviart element approximation for Stekloff eigenvalues in inverse scattering. Adv. Comput. Math. 46 (2020) 1–25. [CrossRef] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.