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Derivative with respect to discontinuities in the porosity. (English. Abridged French version) Zbl 1013.76085

Summary: We investigate the sensitivity of hydrostatic pressure of flows through porous media to the position of soil layers. Indeed, these induce discontinuities of porosity, which is a piecewise constant coefficient \(\kappa\) of partial differential equation satisfied by the pressure \(u\), and it leads to the computation of the derivative of \(u\) with respect to changes in position of discontinuity surfaces of \(\kappa\). The analysis relies on a mixed formulation of the problem. Preliminary numerical simulations are given to illustrate the theory, and an application to a simple inverse problem is also given.

MSC:

76S05 Flows in porous media; filtration; seepage
35Q35 PDEs in connection with fluid mechanics

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References:

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