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 
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/
@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},
     year = {2012},
     volume = {15},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a5/}
}
TY  - JOUR
AU  - A. Burel
AU  - S. Impériale
AU  - P. Joly
TI  - Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2012
SP  - 165
EP  - 174
VL  - 15
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a5/
LA  - ru
ID  - SJVM_2012_15_2_a5
ER  - 
%0 Journal Article
%A A. Burel
%A S. Impériale
%A P. Joly
%T Solving the homogeneous isotropic linear elastodynamics equations using potentials and finite elements. The case of the rigid boundary condition
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2012
%P 165-174
%V 15
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2012_15_2_a5/
%G ru
%F SJVM_2012_15_2_a5

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Achenbach J. D., Wave Propagation in Elastic Solids, American Elsevier, Amsterdam–New York, 1975

[2] Cohen G., Higher-order Numerical Methods for Transient Wave Equations, Springer-Verlag, Berlin, 2001 | MR

[3] Diaz J., Joly P., “Robust high order non-conforming finite element formulation for time domain fluid-structure interaction”, J. of Computational Acoustics. An IMACS Journal, 13:3 (2005), 403–431 | MR | Zbl

[4] Joly P., Ainsworth M., Davies P., Duncan D., Martin P., Rynne B., “Variational methods for time dependant wave propagation problems”, Topics in computational wave propagation: Direct and Inverse Problems. Computational Methods in Wave Propagation, Springer Verlag, Berlin, 2003, 201–264 | MR | Zbl

[5] Joly P., Finite Element Methods with Continuous Displacement, Chapman Hall/CRC, Boca Raton, FL, 2008, 267–329 | MR | Zbl

[6] Monk P., Finite Element Methods for Maxwell's Equations, Oxford science publications, Oxford, 2003 | Zbl