  This work is concerned with an inverse elastic scattering problem of
identifying the unknown rigid obstacle embedded in an open space filled with a
homogeneous and isotropic elastic medium. A Newton-type iteration method
relying on the boundary condition is designed to identify the boundary curve of
the obstacle. Based on the Helmholtz decomposition and the Fourier-Bessel
expansion, we explicitly derive the approximate scattered field and its
derivative on each iterative curve. Rigorous mathematical justifications for
the proposed method are provided. Numerical examples are presented to verify
the effectiveness of the proposed method.
