An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the perfectly matched layer (PML) technique. The well-posedness and exponential convergence of the solution are established for the truncated PML problem by developing an equivalent transparent boundary condition. Second, an a posteriori error estimate is deduced for the discrete problem and is used to determine the finite elements for refinements and to determine the PML parameters. Numerical experiments are included to demonstrate the competitive behavior of the proposed adaptive method.
Accepté le :
DOI : 10.1051/m2an/2017018
Keywords: Elastic wave equation, adaptive finite element, perfectly matched layer, a posteriori error estimate
Jiang, Xue 1 ; Li, Peijun 2 ; Lv, Junliang 3 ; Zheng, Weiying 4
@article{M2AN_2017__51_5_2017_0,
author = {Jiang, Xue and Li, Peijun and Lv, Junliang and Zheng, Weiying},
title = {An adaptive finite element {PML} method for the elastic wave scattering problem in periodic structures},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {2017--2047},
year = {2017},
publisher = {EDP Sciences},
volume = {51},
number = {5},
doi = {10.1051/m2an/2017018},
mrnumber = {3731558},
zbl = {1408.74048},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an/2017018/}
}
TY - JOUR AU - Jiang, Xue AU - Li, Peijun AU - Lv, Junliang AU - Zheng, Weiying TI - An adaptive finite element PML method for the elastic wave scattering problem in periodic structures JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2017 SP - 2017 EP - 2047 VL - 51 IS - 5 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an/2017018/ DO - 10.1051/m2an/2017018 LA - en ID - M2AN_2017__51_5_2017_0 ER -
%0 Journal Article %A Jiang, Xue %A Li, Peijun %A Lv, Junliang %A Zheng, Weiying %T An adaptive finite element PML method for the elastic wave scattering problem in periodic structures %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2017 %P 2017-2047 %V 51 %N 5 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an/2017018/ %R 10.1051/m2an/2017018 %G en %F M2AN_2017__51_5_2017_0
Jiang, Xue; Li, Peijun; Lv, Junliang; Zheng, Weiying. An adaptive finite element PML method for the elastic wave scattering problem in periodic structures. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 2017-2047. doi: 10.1051/m2an/2017018
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