@Article{NMTMA-4-379,
author = {Changhui Yao and Zhonghua Qiao},
title = {Extrapolation of Mixed Finite Element Approximations for the Maxwell Eigenvalue Problem},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2011},
volume = {4},
number = {3},
pages = {379--395},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2011.m1018},
url = {http://global-sci.org/intro/article_detail/nmtma/5974.html}
}