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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Convergence and optimality of adaptive edge finite element methods for time-harmonic Maxwell equations
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by Liuqiang Zhong, Long Chen, Shi Shu, Gabriel Wittum and Jinchao Xu PDF
Math. Comp. 81 (2012), 623-642 Request permission


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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Additional Information
  • Liuqiang Zhong
  • Affiliation: School of Mathematical and Computational Sciences, Xiangtan University, Hunan 411105, China
  • Address at time of publication: School of Mathematics Sciences, South China Normal University, Guangzhou 510631, China
  • Email:
  • Long Chen
  • Affiliation: Department of Mathematics, University of California, Irvine, California 92697
  • MR Author ID: 735779
  • Email:
  • Shi Shu
  • Affiliation: School of Mathematical and Computational Sciences, Xiangtan University, Hunan 411105, China
  • Email:
  • Gabriel Wittum
  • Affiliation: Simulation and Modeling, Goethe Center for Scientific Computing, Goethe-University, Kettenhofweg 139, 60325 Frankfurt am Main, Germany
  • Email:
  • Jinchao Xu
  • Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
  • MR Author ID: 228866
  • Email:
  • Received by editor(s): June 3, 2010
  • Published electronically: December 13, 2011
  • Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (Grant No. 11026091)
    The second author was supported by NSF Grant DMS-0811272 and in part by 2010-2011 UC Irvine CORCL
    The third author was supported in part by NSFC Key Project 11031006, Hunan Provincial Natural Science Foundation of China (Grant No. 10JJ7001), and the Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province of China
    The fourth author was supported in part by the German ministry of Economics and technology, BMWi, and the GRS (Gesellschaft für Reaktorsicherheit).
    The last author was supported in part by NSF Grant DMS-0915153, DMS-0749202 and the Alexander von Humboldt Research Award for Senior US Scientist.
  • © Copyright 2011 American Mathematical Society
  • Journal: Math. Comp. 81 (2012), 623-642
  • MSC (2010): Primary 65F10, 65N30; Secondary 65N12, 78A25
  • DOI:
  • MathSciNet review: 2869030