Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations

Authors: Liuqiang Zhong, Long Chen, Shi Shu, Gabriel Wittum and Jinchao Xu
Journal: Math. Comp. 81 (2012), 623-642
MSC (2010): Primary 65F10, 65N30; Secondary 65N12, 78A25
Posted: December 13, 2011
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider a standard Adaptive Edge Finite Element Method (AEFEM) based on arbitrary order Nédélec edge elements, for three-dimen-
sional indefinite time-harmonic Maxwell equations. We prove that the AEFEM gives a contraction for the sum of the energy error and the scaled error estimator, between two consecutive adaptive loops provided the initial mesh is fine enough. Using the geometric decay, we show that the AEFEM yields the best possible decay rate of the error plus oscillation in terms of the number of degrees of freedom. The main technical contribution of the paper is the establishment of a quasi-orthogonality and a localized a posteriori error estimator.

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