Year: 2011
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 3 : pp. 379–395
Abstract
In this paper, a general method to derive asymptotic error expansion formulas for the mixed finite element approximations of the Maxwell eigenvalue problem is established. Abstract lemmas for the error of the eigenvalue approximations are obtained. Based on the asymptotic error expansion formulas, the Richardson extrapolation method is employed to improve the accuracy of the approximations for the eigenvalues of the Maxwell system from $\mathcal{O}(h^2)$ to $\mathcal{O}(h^4)$ when applying the lowest order Nédélec mixed finite element and a nonconforming mixed finite element. To our best knowledge, this is the first superconvergence result of the Maxwell eigenvalue problem by the extrapolation of the mixed finite element approximation. Numerical experiments are provided to demonstrate the theoretical results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2011.m1018
Numerical Mathematics: Theory, Methods and Applications, Vol. 4 (2011), Iss. 3 : pp. 379–395
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Maxwell eigenvalue problem mixed finite element asymptotic error expansion Richardson extrapolation.
-
Recent results on lower bounds of eigenvalue problems by nonconforming finite element methods
Lin, Qun | Xie, HehuInverse Problems & Imaging, Vol. 7 (2013), Iss. 3 P.795
https://doi.org/10.3934/ipi.2013.7.795 [Citations: 7] -
Superconvergence analysis and extrapolation of a BDF2 fully discrete scheme for nonlinear reaction–diffusion equations
Liang, Conggang | Shi, DongyangCommunications in Nonlinear Science and Numerical Simulation, Vol. 140 (2025), Iss. P.108446
https://doi.org/10.1016/j.cnsns.2024.108446 [Citations: 0] -
Nonconforming Finite Element Method for the Transmission Eigenvalue Problem
Ji, Xia | Xi, Yingxia | Xie, HehuAdvances in Applied Mathematics and Mechanics, Vol. 9 (2017), Iss. 1 P.92
https://doi.org/10.4208/aamm.2015.m1295 [Citations: 12] -
Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods
Luo, FuSheng | Lin, Qun | Xie, HeHuScience China Mathematics, Vol. 55 (2012), Iss. 5 P.1069
https://doi.org/10.1007/s11425-012-4382-2 [Citations: 35] -
A multi-level method for transmission eigenvalues of anisotropic media
Ji, Xia | Sun, JiguangJournal of Computational Physics, Vol. 255 (2013), Iss. P.422
https://doi.org/10.1016/j.jcp.2013.08.030 [Citations: 20]