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Advances in Computational Mathematics

, Volume 41, Issue 5, pp 1131–1157 | Cite as

Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system

  • Immanuel MartiniEmail author
  • Gianluigi Rozza
  • Bernard Haasdonk
Article

Abstract

The coupling of a free flow with a flow through porous media has many potential applications in several fields related with computational science and engineering, such as blood flows, environmental problems or food technologies. We present a reduced basis method for such coupled problems. The reduced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decomposition formulation, namely the Stokes-Darcy problem. Thanks to an offline/online-decomposition, computational times can be drastically reduced. At the same time the induced error can be bounded by fast evaluable a-posteriori error bounds. In the offline-phase the proposed algorithms make use of the decomposed problem structure. Rigorous a-posteriori error bounds are developed, indicating the accuracy of certain lifting operators used in the offline-phase as well as the accuracy of the reduced coupled system. Also, a strategy separately bounding pressure and velocity errors is extended. Numerical experiments dealing with groundwater flow scenarios demonstrate the efficiency of the approach as well as the limitations regarding a-posteriori error estimation.

Keywords

Reduced basis method Stokes flow Porous medium equation Domain decomposition Non-coercive problem Error estimation 

Mathematics Subject Classifications (2010)

65N55 76S05 76D07 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Immanuel Martini
    • 1
    Email author
  • Gianluigi Rozza
    • 2
  • Bernard Haasdonk
    • 1
  1. 1.Institute of Applied Analysis and Numerical SimulationUniversity of StuttgartStuttgartGermany
  2. 2.SISSA MathLabInternational School for Advanced StudiesTriesteItaly

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