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Inverse models to determine the permeability are generally based on existing forward models for the pressure. The permeabilities are adapted in such a way that the calculated pressures match the specified pressures in a number of points. To assimilate a priori knowledge about the flux, we introduce the ‘flux assimilation method’, which is based on the ‘vector potential–pressure formulation’ of Darcy's law. Thanks to an unconventional discretization technique – the ‘edge-based face element method’ – not only the specified pressures, but also specified information about the flux density can easily be assimilated. A relatively simple, but insightful analytical example illustrates the potential of this method.