[1]
Babuška, I. and Aziz, A., Survey Lectures onMathematical Foundations of the Finite Element Method, in The Mathematical Foundations of the Finite Element Method with Application to the Partial Differential Equations, ed. by Aziz, A., Academic Press, New York, 1973, 5–359.

[2]
Bao, G., Li, P., and Wu, H., An adaptive edge element method with perfectly matched absorbing layers for wave scattering by periodic structures, Math. Comp., 79 (2010), 1–34.

[3]
Bao, G. and Wu, H., On the convergence of the solutions of PML equations for Maxwell's equations, SIAM J. Numer. Anal., 43 (2005), 2121–2143.

[4]
Bérenger, J.-P., A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys., 114 (1994), 185–200.

[5]
Bramble, J. H. and Pasciak, J. E., Analysis of a finite PML approximation for the three dimensional time-harmonic Maxwell and acoustic scattering problems, Math. Comp., 76 (2007), 597–614.

[6]
Bramble, J. H., Pasciak, J. E., and Trenev, D., Analysis of a finite PML approximation to the three dimensional elastic wave scattering problem, Math. Comp., 79 (2010), 2079–2101.

[7]
Chen, J. and Chen, Z., An adaptive perfectly matched layer technique for 3-D time-harmonic electromagnetic scattering problems, Math. Comp., 77 (2008), 673–698.

[8]
Chen, Z. and Wu, H., An adaptive finite element method with perfectly matched absorbing layers for the wave scattering by periodic structures, SIAM J. Numer. Anal., 41 (2003), 799–826.

[9]
Chen, Z. and Wu, X., An adaptive uniaxial perfectlymatched layermethod for time-harmonic scattering problems, Numer. Math. Theor. Meth. Appl., 1 (2008), 113–137.

[10]
Chen, Z. and Liu, X., An adptive perfectly matched layer technique for time-harmonic scattering problems, SIAM J. Numer. Anal., 43 (2005), 645–671.

[11]
Chen, Z., Xiang, X., and Zhang, X., Convergence of the PML method for elasticwave scattering problems, Math. Comp., to appear.

[12]
Collino, F. and Monk, P., The perfectly matched layer in curvilinear coordinates, SIAM J. Sci. Comput., 19 (1998), 2061–1090.

[13]
Collino, F. and Tsogka, C., Application of the perfectly matched absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Geophysics, 66 (2001), 294–307.

[14]
Colton, D. and Kress, R., Integral Equation Methods in Scattering Theory, John Wiley & Sons, New York, 1983.

[15]
Chew, W. and Weedon, W., A 3D perfectly matched medium for modified Maxwell's equations with stretched coordinates, Microwave Opt. Techno. Lett., 13 (1994), 599–604.

[16]
Estorff, O. V. and Antes, H., On FEM-BEM coupling for fluid-structure interaction analyses in the time domain, Internat. J. Numer. Methods Engrg., 31 (1991), 1151–1168.

[17]
Flemisch, B., Kaltenbacher, M., and Wohlmuth, B. I., Elasto-acoustic and acoustic-acoustic coupling on non-matching grids, Internat. J. Numer. Methods Engrg., 67 (2006), 1791–1810.

[18]
Gao, Y. and Li, P., Time-domain analysis of an acoustic-elastic interaction problem, preprint.

[19]
Gao, Y., Li, P., and Zhang, B., Analysis of transient acoustic-elastic interaction in an unbounded structure, preprint.

[20]
Hastings, F. D., Schneider, J. B., and Broschat, S. L., Application of the perfectly matched layer (PML) absorbing boundary condition to elastic wave propagation, J. Acoust. Soc. Am., 100 (1996), 3061–3069.

[21]
Hohage, T., Schmidt, F., and Zschiedrich, L., Solving time-harmonic scattering problems based on the pole condition. II: Convergence of the PML method, SIAM J. Math. Anal., 35 (2003), 547–560.

[22]
Hsiao, G. C., On the boundary-field equation methods for fluid-structure interactions, In Problems and methods in mathematical physics (Chemnitz, 1993), vol. 134, Teubner-Texte Math., 79–88, Teubner, Stuttgart, 1994.

[23]
Hsiao, G. C., Kleinman, R. E., and Schuetz, L. S., On variational formulations of boundary value problems for fluid-solid interactions, In Elastic wave propagation (Galway, 1988), vol. 35, North-Holland Ser. Appl. Math. Mech., 321–326, North-Holland, Amsterdam, 1989.

[24]
Hsiao, G. C., Sánchez-Vizuet, T., and Sayas, F.-J., Boundary and coupled boundary-finite element methods for transient wave-structure interaction, IMA J. Numer. Anal., 37 (2017), 237–265.

[25]
Jiang, X., Li, P., Lv, J., and Zheng, W., An adaptive finite element PML method for the elastic wave scattering problem in periodic structure, ESAIM: Math. Model. Numer. Anal., to appear.

[26]
Jiang, X., Li, P., Lv, J., and Zheng, W., Convergence of the PML solution for elastic wave scattering by biperiodic structures, preprint.

[27]
Lassas, M. and Somersalo, E., On the existence and convergence of the solution of PML equations, Computing, 60 (1998), 229–241.

[28]
Luke, C. J. and Martin, P. A., Fluid-solid interaction: acoustic scattering by a smooth elastic obstacle, SIAM J. Appl. Math., 55 (1995), 904–922.

[30]
Scott, L. R. and Zhang, S., Finite element interpolation of nonsmooth functions satisfying boundary conditions, Math. Comp., 54 (1990), 483–493.

[31]
Soares, D. and Mansur, W., Dynamic analysis of fluid-soil-structure interaction problems by the boundary element method, J. Comput. Phys., 219 (2006), 498–512.

[32]
Turkel, E. and Yefet, A., Absorbing PML boundary layers for wave-like equations, Appl. Numer. Math., 27 (1998), 533–557.