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

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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 technolo gies. We present a reduced basis method for such coupled problems. The re duced basis method is a model order reduction method applied in the context of parametrized systems. Our approach is based on a heterogeneous domain decompo sition 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 accu racy 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
Reduced basis method, Stokes flow, Porous medium equation, Domain decomposition, Non-coercive problem, Error estimation