An adaptive finite element method is presented for the elastic scattering ofa time-harmonic plane wave by a periodic surface. First, the unbounded physicaldomain is truncated into a bounded computational domain by introducing theperfectly matched layer (PML) technique. The well-posedness and exponentialconvergence of the solution are established for the truncated PML problem bydeveloping an equivalent transparent boundary condition. Second, an aposteriori error estimate is deduced for the discrete problem and is used todetermine the finite elements for refinements and to determine the PMLparameters. Numerical experiments are included to demonstrate the competitivebehavior of the proposed adaptive method.
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