On the Direct and Inverse Transmission Problems in Elasticity

In this paper, we investigate the direct and inverse elastic scattering problems of a time-harmonic elastic wave from a bounded penetrable elastic body. A finite element method based on the Dirichlet-to-Neumann operator is developed, and its corresponding error analysis is provided. For the inverse problem, a Newton-type iterative method is proposed to reconstruct the shape of the elastic body from scattered field measurements taken both inside and outside the interface boundary. Numerical experiments are presented to illustrate the effectiveness of the proposed approach.