Albella Martínez, JorgeImperiale, SebastienJoly, PatrickRodríguez García, Jerónimo2024-02-092024-02-092018Albella Martínez, J., Imperiale, S., Joly, P., & Rodríguez, J. (2018). Solving 2D Linear Isotropic Elastodynamics by Means of Scalar Potentials: A New Challenge for Finite Elements. Journal of Scientific Computing, 77(3), 1832-1873. https://doi.org/10.1007/S10915-018-0768-90885-7474http://hdl.handle.net/10347/32706This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10915-018-0768-9In this work we present a method for the computation of numerical solutions of 2D homogeneous isotropic elastodynamics equations by solving scalar wave equations. These equations act on the potentials of a Helmholtz decomposition of the displacement field and are decoupled inside the propagation domain. We detail how these equations are coupled at the boundary depending on the nature of the boundary condition satisfied by the displacement field. After presenting the case of rigid boundary conditions, that presents no specific difficulty, we tackle the challenging case of free surface boundary conditions that presents severe stability issues if a straightforward approach is used. We introduce an adequate functional framework as well as a time domain mixed formulation to circumvent these issues. Numerical results confirm the stability of the proposed approach.engCopyright © 2018, Springer Science Business Media, LLC, part of Springer Naturehttp://creativecommons.org/licenses/by-nc-nd/4.0/Elastic wave propagationHelmholtz decompositionPotentialsStability of the evolution problemjournal article10.1007/s10915-018-0768-91573-7691open access