### Plenary Lecture 7: Double obstacle phase field approach for an elliptic inverse problem with discontinuous coefficients

Deckelnick, K *(Otto-von-Guericke-Universität Magdeburg)*

Wednesday 25 June 2014, 13:30-14:15

Seminar Room 1, Newton Institute

#### Abstract

We consider the inverse problem of recovering interfaces where the diffusion coefficient in an elliptic PDE has jump discontinuities. We employ a least squares approach together with a perimeter regularization. A suitable relaxation of the perimeter leads to a sequence of Cahn--Hilliard type functionals for which we obtain a $\Gamma$--convergence result. Using a finite element discretization of the elliptic PDE and a suitable
adjoint problem we derive an iterative method in order to approximate discrete critical points. We prove convergence of the iteration and present results of numerical tests.
This is joint work with C.M. Elliott (Warwick) and V. Styles (Sussex).

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