Artificial conditions for the linear elasticity equations

Bonnaillie-Noël, Virginie; Dambrine, Marc; Hérau, Frédéric; Vial, Grégory

doi:10.1090/S0025-5718-2014-02901-3

Artificial conditions for the linear elasticity equations
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by Virginie Bonnaillie-Noël, Marc Dambrine, Frédéric Hérau and Grégory Vial PDF

Math. Comp. 84 (2015), 1599-1632 Request permission

Abstract:

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 us to consider near-circular domains. We complete the analysis by some numerical simulations.

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