Abstract
Consider the scattering of a time-harmonic acoustic incident wave by a bounded, penetrable and isotropic elastic solid, which is immersed in a homogeneous compressible air/fluid. By the Dirichlet-to-Neumann (DtN) operator, an exact transparent boundary condition is introduced and the model is formulated as a boundary value problem of acoustic-elastic interaction. Based on a duality argument technique, an a posteriori error estimate is derived for the finite element method with the truncated DtN boundary operator. The a posteriori error estimate consists of the finite element approximation error and the truncation error of the DtN boundary operator, where the latter decays exponentially with respect to the truncation parameter. An adaptive finite element algorithm is proposed for solving the acoustic-elastic interaction problem, where the truncation parameter is determined through the truncation error and the mesh elements for local refinements are chosen through the finite element discretization error. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.
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Acknowledgements
This work of J.L. was partially supported by the National Natural Science Foundation of China grant 12271209 and Jilin Province Science and Technology Plan Development Project grant 20210201078GX.
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Lin, L., Lv, J. & Li, S. An adaptive finite element DtN method for the acoustic-elastic interaction problem. Adv Comput Math 50, 67 (2024). https://doi.org/10.1007/s10444-024-10160-5
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DOI: https://doi.org/10.1007/s10444-024-10160-5
Keywords
- Acoustic-elastic interaction problem
- Adaptive finite element method
- Transparent boundary condition
- A posteriori error estimate