We treat the inverse problem of determining material losses, such as
cavities, in a conducting body, by performing electrostatic measurements at the
boundary. We develop a numerical approach, based on variational methods, to
reconstruct the unknown material loss by a single boundary measurement of
current and voltage type.
The method is based on the use of phase-field functions to model the material
losses and on a perimeter-like penalization to regularize the otherwise
ill-posed problem.We justify the proposed approach by a convergence result, as
the error on the measurement goes to zero.Comment: 28 page