Factorization method for the inverse Stokes problem

Armin Lechleiter; Tobias Rienmüller

doi:10.3934/ipi.2013.7.1271

Article Contents

2013, Volume 7, Issue 4: 1271-1293. Doi: 10.3934/ipi.2013.7.1271

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Factorization method for the inverse Stokes problem

Armin Lechleiter^1, and
Tobias Rienmüller^1,

1.
Zentrum für Technomathematik, Universität Bremen, 28359 Bremen

Received: December 31, 2012

Revised: July 31, 2013

Published: October 2013

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Abstract

We propose an imaging technique for the detection of porous inclusions in a stationary flow based on the Factorization method. The stationary flow is described by the Stokes-Brinkmann equations, a standard model for a flow through a (partially) porous medium, involving the deformation tensor of the flow and the permeability tensor of the porous inclusion. On the boundary of the domain we prescribe Robin boundary conditions that provide the freedom to model, e.g., in- or outlets for the flow. The direct Stokes-Brinkmann problem to find a velocity field and a pressure for given boundary data is a mixed variational problem lacking coercivity due to the indefinite pressure part. It is well-known that indefinite problems are difficult to tackle theoretically using Factorization methods. Interestingly, the Factorization method can nevertheless be applied to this non-coercive problem, as long as one uses data consisting only of velocity measurements. We provide numerical experiments showing the feasibility of the proposed technique.

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Mathematics Subject Classification: Primary: 35R30, 65N21; Secondary: 76D07.

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