%0 Journal Article %J Journal of Scientific Computing %D 2018 %T Certified Reduced Basis Approximation for the Coupling of Viscous and Inviscid Parametrized Flow Models %A Immanuel Martini %A Bernard Haasdonk %A Gianluigi Rozza %B Journal of Scientific Computing %V 74 %P 197-219 %G eng %U https://www.scopus.com/inward/record.uri?eid=2-s2.0-85017156114&doi=10.1007%2fs10915-017-0430-y&partnerID=40&md5=023ef0bb95713f4442d1fa374c92a964 %R 10.1007/s10915-017-0430-y %0 Journal Article %J Advances in Computational Mathematics %D 2015 %T Reduced basis approximation and a-posteriori error estimation for the coupled Stokes-Darcy system %A Immanuel Martini %A Gianluigi Rozza %A Bernard Haasdonk %K Domain decomposition %K Error estimation %K Non-coercive problem %K Porous medium equation %K Reduced basis method %K Stokes flow %X

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.

%B Advances in Computational Mathematics %V special issue for MoRePaS 2012 %G eng %N in press %R 10.1007/s10444-014-9396-6