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.

@ARTICLE{MartiniRozzaHaasdonk2015,
author = {Martini, Immanuel and Rozza, Gianluigi and Haasdonk, Bernard},
title = {Reduced basis approximation and a-posteriori error estimation for
the coupled {S}tokes-{D}arcy system},
journal = {Advances in Computational Mathematics},
year = {2015},
volume = {41},
pages = {1131--1157},
number = {5},
doi = {10.1007/s10444-014-9396-6},
issn = {1572-9044},
}