Lacking Data Recovery via Partially Overdetermined Boundary Conditions in Linear Elasticity

Artificial boundary conditions to compute correctors in linear elasticity

Linear Advection with Ill-posed Boundary Conditions via L-minimization

The goal of this paper is to explain a phenomenon that has been reported in [4]; namely, finite-element-based best L-approximations seem to converge to viscosity solutions of some classes of first-order PDE’s. In particular we prove in this paper that it is indeed the case in dimension one for the linear transport equation equipped with a set of ill-posed boundary conditions. To explain our int...

Integrability of Displacement and Stresses in Linear and Nonlinear Elasticity with Mixed Boundary Conditions

Equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered. The bounded domain is assumed to have a Lipschitz boundary and to satisfy additional regularity assumptions. W 1,p regularity for the displacements and Lp regularity for the stresses is proved for some p > 2.

On the Compatibility Equations of Nonlinear and Linear Elasticity in the Presence of Boundary Conditions∗

We use Hodge-type orthogonal decompositions for studying the compatibility equations of the displacement gradient and the linear strain with prescribed boundary displacements. We show that the displacement gradient is compatible if and only if for any equilibrated virtual first-Piola Kirchhoff stress tensor field, the virtual work done by the displacement gradient is equal to the virtual work d...

Artificial conditions for the linear elasticity equations

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 wellposedness except for a countable set of parameters. A perturbation...