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An optimal adaptive mixed finite element method


Authors: 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
Published electronically: August 16, 2010
MathSciNet review: 2772091
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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

DOI: https://doi.org/10.1090/S0025-5718-2010-02397-X
Keywords: AFEM, adaptive mixed finite element method, AMFEM, optimal convergence
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’
Article copyright: © Copyright 2010 Carsten Carstensen and Hella Rabus