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This article develops the numerical and theoretical study of a reconstructionalgorithm of a potential in a wave equation from boundary measurements, using acost functional built on weighted energy terms coming from a Carleman estimate.More precisely, this inverse problem for the wave equation consists in thedetermination of an unknown time-independent potential from a singlemeasurement of the Neumann derivative of the solution on a part of theboundary. While its uniqueness and stability properties are already well knownand studied, a constructive and globally convergent algorithm based on Carlemanestimates for the wave operator was recently proposed in [L. Baudouin, M. deBuhan and S. Ervedoza, Global carleman estimates for waves and applications,Comm. Partial Differential Equations 38 (2013), no. 5]. However, the numericalimplementation of this strategy still presents several challenges, that wepropose to address here.

Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation