2022
DOI: 10.48550/arxiv.2205.15626
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A Reduced Basis Method for Darcy flow systems that ensures local mass conservation by using exact discrete complexes

Abstract: A solution technique is proposed for flows in porous media that guarantees local conservation of mass. We first compute a flux field to balance the mass source and then exploit exact co-chain complexes to generate a solenoidal correction. A reduced basis method based on proper orthogonal decomposition is employed to construct the correction and we show that mass balance is ensured regardless of the quality of the reduced basis approximation. The method is directly applicable to mixed finite and virtual element… Show more

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