Geodesic
An adaptive finite element PML method for the elastic wave scattering problem in periodic structures
Jiang, Xue1 ; Li, Peijun2  ; Lv, Junliang3 ; Zheng, Weiying4
1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China.
2 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.
3 School of Mathematics, Jilin University, Changchun 130012, P.R. China.
4 LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Science, University of Chinese Academy of Sciences, 100190, P.R. China.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 51 (2017) no. 5, pp. 2017-2047

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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.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017018
Classification : 65N30, 78A45, 35Q60
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

1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, P.R. China.
2 Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA.
3 School of Mathematics, Jilin University, Changchun 130012, P.R. China.
4 LSEC, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences; School of Mathematical Science, University of Chinese Academy of Sciences, 100190, P.R. China. 
@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},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {5},
     year = {2017},
     doi = {10.1051/m2an/2017018},
     mrnumber = {3731558},
     zbl = {1408.74048},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an/2017018/}
}
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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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