We examine the problem of Identifying both the location and constitutive law governing electrical current flow across a one-dimensional linear crack in a two dimensional region when the crack only partially blocks the flow of current. We develop a a constructive numerical procedure for solving the inverse problem and provide computational examples.
Ogborne, F Ronald III and Vellela, Melissa E., "Reconstruction of Cracks with Unknown Transmission Condition from Boundary Data" (2002). Mathematical Sciences Technical Reports (MSTR). 104.