@article {2018,
	title = {Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models},
	journal = {Journal of Scientific Computing},
	volume = {74},
	year = {2018},
	pages = {197-219},
	doi = {10.1007/s10915-017-0430-y},
	url = {https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114\&doi=10.1007\%2fs10915-017-0430-y\&partnerID=40\&md5=023ef0bb95713f4442d1fa374c92a964},
	author = {Immanuel Martini and Bernard Haasdonk and Gianluigi Rozza}
}
@article {2015,
	title = {Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system},
	journal = {Advances in Computational Mathematics},
	volume = {special issue for MoRePaS 2012},
	year = {2015},
	abstract = {<p>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.</p>},
	keywords = {Domain decomposition, Error estimation, Non-coercive problem, Porous medium equation, Reduced basis method, Stokes flow},
	issn = {1019-7168},
	doi = {     10.1007/s10444-014-9396-6},
	author = {Immanuel Martini and Gianluigi Rozza and Bernard Haasdonk}
}
