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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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An optimal adaptive mixed finite element method
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by Carsten Carstensen and Hella Rabus PDF
Math. Comp. 80 (2011), 649-667

Abstract:

Various applications in fluid dynamics and computational continuum mechanics motivate the development of reliable and efficient adaptive algorithms for mixed finite element methods. In order to save degrees of freedom, not all but just a selection of finite element domains are refined. Hence the fundamental question of convergence as well as the question of optimality require new mathematical arguments. The presented adaptive algorithm for Raviart-Thomas mixed finite element methods solves the Poisson model problem, with optimal convergence rate.
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Additional Information
  • Carsten Carstensen
  • Affiliation: Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany and Department of Computational Science and Engineering, Yonsei University, 120-749 Seoul, Korea
  • Email: cc@mathematik.hu-berlin.de
  • Hella Rabus
  • Affiliation: Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
  • Email: rabus@mathematik.hu-berlin.de
  • Received by editor(s): September 16, 2008
  • Received by editor(s) in revised form: July 26, 2009, and November 16, 2009
  • Published electronically: August 16, 2010
  • Additional Notes: The first author was partly supported by the Hausdorff Institute of Mathematics in Bonn, Germany and by the WCU program through KOSEF (R31-2008-000-10049-0)
    The second author was partly supported by the DFG Research Center MATHEON “Mathematics for key technologies” in Berlin, Germany and the DFG research group 797 ‘Analysis and Computation of Microstructure in Finite Plasticity’
  • © Copyright 2010 Carsten Carstensen and Hella Rabus
  • Journal: Math. Comp. 80 (2011), 649-667
  • MSC (2010): Primary 65N12, 65N15, 65N30, 65N50, 65Y20
  • DOI: https://doi.org/10.1090/S0025-5718-2010-02397-X
  • MathSciNet review: 2772091