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We deal with a boundary detection problem arising in nondestructive testingof materials. The problem consists in recovering an unknown portion of theboundary, where a Robin condition is satisfied, with the use of a Cauchy datapair collected on the accessible part of the boundary. We combine alinearization argument with a Tikhonov regularization approach for the localreconstruction of the unknown defect. Moreover, we discuss the regularizationparameter choice by means of the so called balancing principle and we presentsome numerical tests that show the efficiency of our method.

Discretized Tikhonov regularization for Robin boundaries localization