  Consider the elastic scattering of an incident wave by a rigid obstacle in
three dimensions, which is formulated as an exterior problem for the Navier
equation. By constructing a Dirichlet-to-Neumann (DtN) operator and introducing
a transparent boundary condition, the scattering problem is reduced
equivalently to a boundary value problem in a bounded domain. The discrete
problem with the truncated DtN operator is solved by using the a posteriori
error estimate based adaptive finite element method. The estimate takes account
of both the finite element approximation error and the truncation error of the
DtN operator, where the latter is shown to converge exponentially with respect
to the truncation parameter. Moreover, the generalized Woodbury matrix identity
is utilized to solve the resulting linear system efficiently. Numerical
experiments are presented to demonstrate the superior performance of the
proposed method.
