Theoretical and numerical results for parameter estimation in nonlinear elastomers

In this paper we present an approximation framework and theoretical convergence results for a class of parameter estimation problems for general abstract nonlinear hyperbolic systems. Included as special cases are convergence results for general approximation families for the forward solution of the nonlinear systems. These systems include as a special case those modeling a large class of nonlinear elastomers. Numerical results are presented to illustrate the convergence of spline based methods in the context of the approximation framework.