RT Journal Article
T1 Numerical analysis of a method for solving 2D linear isotropic elastodynamics with traction free boundary condition using potentias and finite elements
A1 Albella Martínez, Jorge
A1 Imperiale, Sebastien
A1 Joly, Patrick
A1 Rodríguez García, Jerónimo
K1 CFL condition
K1 Elastic wave propagation
K1 Helmholtz decomposition
K1 Mass lumping
K1 Numerical analysis
K1 Potentials
K1 Stability of the evolution problem
AB When solving 2D linear elastodynamic equations in homogeneous isotropic media, a Helmholtz decomposition of the displacement field decouples the equations into two scalar wave equations that only interact at the boundary. It is then natural to look for numerical schemes that independently solve the scalar equations and couple the solutions at the boundary. The case of rigid boundary condition was treated by Burel [Ph.D. thesis, Université Paris Sud-Paris XI (2014)] and Burel et al. [Numer. Anal. Appl. 5 (2012), pp. 136— 143]. However the case of traction free boundary condition was proven by Martinez et al. [J. Sci. Comput. 77 (2018), pp. 1832-1873] to be unstable if a straightforward approach is used. Then an adequate functional framework as well as a time domain mixed formulation to circumvent these issues was presented. In this work we first review the formulation presented by Martinez et al. [J. Sci. Comput. 77 (2018), pp. 1832-1873] and propose a subsequent discretised formulation. We provide the complete stability analysis of the corresponding numerical scheme. Numerical results that illustrate the theory are also shown.
PB American Mathematical Society
SN 0025-5718
YR 2021
FD 2021
LK http://hdl.handle.net/10347/32713
UL http://hdl.handle.net/10347/32713
LA eng
NO Martínez, J. A., Imperiale, S., Joly, P., & Rodríguez, J. (2021). Numerical analysis of a method for solving 2D linear isotropic elastodynamics with traction free boundary condition using potentias and finite elements. Mathematics of Computation, 90(330), 1589-1636. https://doi.org/10.1090/MCOM/3613
NO The first and fourth authors were supported in part by FEDER/Ministerio de Ciencia, Inno-vación y Universidades and Agencia Estatal de Investigación through grants MTM2013-43745-R and MTM2017-86459-R and by Xunta de Galicia through grant ED431C 2017/60.
DS Minerva
RD 27 abr 2026