Geodesic
Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 165-174

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In this article, elastic wave propagation in a homogeneous isotropic elastic medium with a rigid boundary is considered. A method based on the decoupling of pressure and shear waves via the use of scalar potentials is proposed. This method is adapted to a finite element discretization, which is discussed. A stable, energy preserving numerical scheme is presented, as well as 2D numerical results. 
@article{SJVM_2012_15_2_a5,
     author = {A. Burel and S. Imp\'eriale and P. Joly},
     title = {Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. {The} case of the rigid boundary condition},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {165--174},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a5/}
}
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A. Burel; S. Impériale; P. Joly. Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 15 (2012) no. 2, pp. 165-174. http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a5/