Commun. Comput. Phys., 13 (2013), pp. 559-582.

Adaptive hp-Finite Element Computations for Time-Harmonic Maxwell's Equations

Xue Jiang 1, Linbo Zhang 1, Weiying Zheng 1*

1 LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China.

Received 23 November 2011; Accepted (in revised version) 9 March 2012
Available online 3 August 2012


In this paper, hp-adaptive finite element methods are studied for time-harmonic Maxwell's equations. We propose the parallel hp-adaptive algorithms on conforming unstructured tetrahedral meshes based on residual-based a posteriori error estimates. Extensive numerical experiments are reported to investigate the efficiency of the hp-adaptive methods for point singularities, edge singularities, and an engineering benchmark problem of Maxwell's equations. The hp-adaptive methods show much better performance than the h-adaptive method.

AMS subject classifications: 65M30, 78A45

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Key words: hp-adaptive finite element method, Maxwell's equations, eddy current problem, a posteriori error estimate.

*Corresponding author.
Email: (X. Jiang), (L. Zhang), (W. Zheng)

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