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A mortar edge element method with nearly optimal convergence for three-dimensional Maxwell's equations


Authors: Qiya Hu, Shi Shu and Jun Zou
Journal: Math. Comp. 77 (2008), 1333-1353
MSC (2000): Primary 65N30, 65N55
DOI: https://doi.org/10.1090/S0025-5718-08-02057-7
Published electronically: January 11, 2008
MathSciNet review: 2398771
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Abstract: In this paper, we are concerned with mortar edge element methods for solving three-dimensional Maxwell's equations. A new type of Lagrange multiplier space is introduced to impose the weak continuity of the tangential components of the edge element solutions across the interfaces between neighboring subdomains. The mortar edge element method is shown to have nearly optimal convergence under some natural regularity assumptions when nested triangulations are assumed on the interfaces. A generalized edge element interpolation is introduced which plays a crucial role in establishing the nearly optimal convergence. The theoretically predicted convergence is confirmed by numerical experiments.


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Additional Information

Qiya Hu
Affiliation: LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematical and System Sciences, The Chinese Academy of Sciences, Beijing 100080, China
Email: hqy@lsec.cc.ac.cn

Shi Shu
Affiliation: School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, China
Email: shushi@xtu.edu.cn

Jun Zou
Affiliation: Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
Email: zou@math.cuhk.edu.hk

DOI: https://doi.org/10.1090/S0025-5718-08-02057-7
Keywords: Maxwell's equations, N\'ed\'elec finite elements, domain decomposition, nonmatching grids, generalized interpolation, error estimate
Received by editor(s): February 3, 2005
Received by editor(s) in revised form: March 28, 2007
Published electronically: January 11, 2008
Additional Notes: The work of the first author was supported by the Natural Science Foundation of China G10371129, the Key Project of Natural Science Foundation of China G10531080, and the National Basic Research Program of China G2005CB321702
The work of the second author was partially supported by the grant (2005CB321702)
The work of the third author was substantially supported by Hong Kong RGC grants (Project 404407 and Project 404606)
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.