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A solution technique is proposed for flows in porous media that guaranteeslocal conservation of mass. We first compute a flux field to balance the masssource and then exploit exact co-chain complexes to generate a solenoidalcorrection. A reduced basis method based on proper orthogonal decomposition isemployed to construct the correction and we show that mass balance is ensuredregardless of the quality of the reduced basis approximation. The method isdirectly applicable to mixed finite and virtual element methods, among otherstructure-preserving discretization techniques, and we present the extension toDarcy flow in fractured porous media.

A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes