22-24 September 2021
Alpen-Adria-Universität Klagenfurt
Europe/Vienna timezone

Monotonicity-Based Regularization for Shape Reconstruction in Linear Elasticity

22 Sep 2021, 11:20
HS 1 (Alpen-Adria-Universität Klagenfurt)

HS 1

Alpen-Adria-Universität Klagenfurt


Sarah Eberle (Goethe University Frankfurt)


We deal with the shape reconstruction of inclusions in elastic bodies and solve the inverse problem by means of a monotonicity-based regularization. In more detail, we show how the monotonicity methods can be converted into a regularization method for a data-fitting functional without losing the convergence properties of the monotonicity methods. In doing so, we introduce constraints on the minimization problem of the residual based on the monotonicity methods and prove the existence and uniqueness of a minimizer as well as the convergence of the method for noisy data. In addition, we compare numerical reconstructions of inclusions based on the monotonicity-based regularization with a standard approach (one-step linearization with Tikhonov-like regularization), which also shows the robustness of our method regarding noise in practice.

Primary author

Sarah Eberle (Goethe University Frankfurt)


Bastian Harrach (Goethe University Frankfurt)

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