A minimum norm interpolation method for determining the displacement field of a homogeneous isotropic elastic body from discrete data

A minimum norm interpolation method is proposed for solving the classical displacement boundary value problem of elastostatics from discretely defined boundary displacement vectors. A stability theorem is developed which is dependent on the spacing of the data on the boundary, and convergence is established for the case in which the data points become dense. A basic tool is a new vectorial generalization of the addition theorem for spherical harmonics