Consider a time-harmonic acoustic plane wave incident onto an elastic body
with an unbounded periodic surface. The medium above the surface is supposed to
be filled with a homogeneous compressible inviscid air/fluid of constant mass
density, while the elastic body is assumed to be isotropic and linear. Di
introducing the Dirichlet-to-Neumann (DtN) operators for acoustic and elastic
waves simultaneously, the model is formulated as an acoustic-elastic
interaction problem in periodic structures. Based on a duality argument, an a
posteriori error estimate is derived for the associated truncated finite
element approximation. The a posteriori error estimate consists of the finite
element approximation error and the truncation error of two different DtN
operators, where the latter decays exponentially with respect to the truncation
parameter. Based on the a posteriori error, an adaptive finite element
algorithm is proposed for solving the acoustic-elastic interaction problem in
periodic structures. Numerical experiments are presented to demonstrate the
effectiveness of the proposed algorithm.

Questo articolo esplora i giri e le loro implicazioni.

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