| Issue |
ESAIM: M2AN
Volume 53, Number 1, January–February 2019
|
|
|---|---|---|
| Page(s) | 85 - 103 | |
| DOI | https://doi.org/10.1051/m2an/2018043 | |
| Published online | 02 April 2019 | |
Research Article
A variant of the plane wave least squares method for the time-harmonic Maxwell’s equations
1
LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China
2
School of Mathematical Sciences, University of Chinese Academy of Sciences, 100049 Beijing, China
* Corresponding author: hqy@lsec.cc.ac.cn; songrongrong@lsec.cc.ac.cn
Received:
13
December
2017
Accepted:
29
June
2018
In this paper we are concerned with the plane wave method for the discretization of time-harmonic Maxwell’s equations in three dimensions. As pointed out in Hiptmair et al. (Math. Comput. 82 (2013) 247–268), it is difficult to derive a satisfactory L2 error estimate of the standard plane wave approximation of the time-harmonic Maxwell’s equations. We propose a variant of the plane wave least squares (PWLS) method and show that the new plane wave approximations yield the desired L2 error estimate. Moreover, the numerical results indicate that the new approximations have sightly smaller L2 errors than the standard plane wave approximations. More importantly, the results are derived for more general models in inhomogeneous media.
Mathematics Subject Classification: 65N30 / 65N55
Key words: Maxwell’s equations / plane wave method / variational problem / L2 error estimate
© The authors. Published by EDP Sciences, SMAI 2019
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