Artificial conditions for the linear elasticity equations

Virginie Bonnaillie-Noël (1) , Marc Dambrine (2) , Frédéric Herau (3) , Grégory Vial (4)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
3 LMJL - Laboratoire de Mathématiques Jean Leray
4 ICJ - Institut Camille Jordan

In this paper, we consider the equations of linear elasticity in an exterior domain. We exhibit artificial boundary conditions on a circle, which lead to a non-coercive second order boundary value problem. In the particular case of an axisymmetric geometry, explicit computations can be performed in Fourier series proving the well-posedness except for a countable set of parameters. A perturbation argument allows to consider near-circular domains. We complete the analysis by some numerical simulations.

Mots clés: spectral theory; Linear elasticity equations; singular perturbation; artificial boundary conditions; Ventcel condition; Dirichlet-to-Neumann map; spectral theory.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]

Virginie Bonnaillie-Noël, Marc Dambrine, Frédéric Herau, Grégory Vial. Artificial conditions for the linear elasticity equations. 2012. ⟨hal-00763441v1⟩