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.
Email: firstname.lastname@example.org (X. Jiang), email@example.com (L. Zhang), firstname.lastname@example.org (W. Zheng)