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arXiv · 1905.04143

Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structures

Peijun Li·Xiaokai Yuan
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Abstract

Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary condition (TBC) is introduced to reduce the scattering problem into a boundary value problem in a bounded domain. By using the finite element method, the discrete problem is considered, where the TBC is replaced by the truncated DtN map. A new duality argument is developed to derive the a posteriori error estimate, which contains both the finite element approximation error and the DtN truncation error. An a posteriori error estimate based adaptive finite element algorithm is developed to solve the elastic surface scattering problem. Numerical experiments are presented to demonstrate the effectiveness of the proposed method.

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Peijun Li, Xiaokai Yuan. 2019-05-09. Convergence of an adaptive finite element DtN method for the elastic wave scattering by periodic structures. https://doi.org/10.1016/j.cma.2019.112722

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