Resolution guarantees for the reconstruction of inclusions in linear elasticity based on monotonicity methods

Abstract

We deal with the reconstruction of inclusions in elastic bodies based on monotonicity methods and construct conditions under which a resolution for a given partition can be achieved. These conditions take into account the background error as well as the measurement noise. We want to highlight that we consider Lamé parameters that are either both smaller or larger than the background Lamé parameters. Both those cases are investigated for standard and linearized monotonicity tests resulting in four different algorithms and the corresponding resolution guarantees.