A spline-based parameter estimation technique for static models of elastic structures

We consider the problem of identifying the spatially varying coefficient of elasticity using an observed solution to the forward problem. Under appropriate conditions this problem can be treated as a first-order hyperbolic equation in the unknown coefficient. We develop some continuous dependence results for this problem and propose a spline-based technique for approximating the unknown coefficient based on these results. We establish the convergence of our numerical scheme and obtain error estimates.