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Hierarchical decomposition of domains with fractures


Authors: Susanna Gebauer, Ralf Kornhuber and Harry Yserentant
Journal: Math. Comp. 75 (2006), 73-90
MSC (2000): Primary 65N55
DOI: https://doi.org/10.1090/S0025-5718-05-01792-8
Published electronically: October 3, 2005
MathSciNet review: 2176390
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Abstract: We consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occurring on a network of thin fractures. We present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix. Upper estimates for the convergence rates are independent of the width of the fractures and of the jumps of the coefficients. Inexact solution of the local subproblems is also considered. The theoretical results are illustrated by numerical experiments.


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Additional Information

Susanna Gebauer
Affiliation: Freie Universität Berlin, Institut für Mathematik II, Arnimallee 2-6, D - 14195 Ber- lin, Germany
Email: susanna.gebauer@math.fu-berlin.de

Ralf Kornhuber
Affiliation: Freie Universität Berlin, Institut für Mathematik II, Arnimallee 2-6, D - 14195 Ber- lin, Germany
Email: kornhuber@math.fu-berlin.de

Harry Yserentant
Affiliation: Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, D-10632 Berlin, Germany
Email: yserentant@math.tu-berlin.de

DOI: https://doi.org/10.1090/S0025-5718-05-01792-8
Received by editor(s): October 25, 2004
Received by editor(s) in revised form: February 8, 2005
Published electronically: October 3, 2005
Additional Notes: This work has been funded in part by the Deutsche Forschungsgemeinschaft under contract Ko 1806/2-1 and Ko 1806/2-3
Article copyright: © Copyright 2005 American Mathematical Society

American Mathematical Society