On regularization and discretization control for the numerical solution of inverse problems in parabolic equations

In this paper, the influence of modelling, a priori information, discretization and measurement error to the numerical solution of inverse problems is investigated. Given an a priori approximation of the unknown parameter function in a parabolic problem, we propose a strategy for the regularized determination of a skeleton solution to the inverse problem. This strategy is based on a discretization control of the forward problem in order to find a trade-off between accuracy and computational efficiency. Numerical results with regard to a nonlinear inverse heat conduction problem illustrate the study.