Error estimates for the finite element approximation of linear elastic equations in an unbounded domain

In this paper we present error estimates for the finite element approximati on of linear elastic equations in an unbounded domain. The finite element a pproximation is formulated on a bounded computational domain using a nonloc al approximate artificial boundary condition or a local one. In fact there are a family of nonlocal approximate boundary conditions with increasing ac curacy (and computational cost) and a family of local ones for a given arti ficial boundary. Our error estimates show how the errors of the finite elem ent approximations depend on the mesh size, the terms used in the approxima te artificial boundary condition, and the location of the artificial bounda ry. A numerical example for Navier equations outside a circle in the plane is presented. Numerical results demonstrate the performance of our error es timates.