  The Navier equation is the governing equation of elastic waves, and computing
its solution accurately and rapidly has a wide range of applications in
geophysical exploration, materials science, etc. In this paper, we focus on the
efficient and high-precision numerical algorithm for the time harmonic elastic
wave scattering problems from cornered domains via the boundary integral
equations in two dimensions. The approach is based on the combination of
Nystr\"om discretization, analytical singular integrals and kernel-splitting
method, which results in a high-order solver for smooth boundaries. It is then
combined with the recursively compressed inverse preconditioning (RCIP) method
to solve elastic scattering problems from cornered domains. Numerical
experiments demonstrate that the proposed approach achieves high accuracy, with
stabilized errors close to machine precision in various geometric
configurations. The algorithm is further applied to investigate the asymptotic
behavior of density functions associated with boundary integral operators near
corners, and the numerical results are highly consistent with the theoretical
formulas.
