A new approach to convergence rate analysis of Tikhonov regularization for parameter identification in heat conduction

Abstract

In this paper we investigate the stability and convergence rates of the widely used output least-squares method with Tikhonov regularization for the identification of the conductivity distribution in a heat conduction system. Due to the rather restrictive source conditions and regularity assumptions on the nonlinear parameter-to-solution operator concerned, the existing Tikhonov regularization theory for nonlinear inverse problems is difficult to apply for the convergence rate analysis here. By introducing some new techniques, we are able to relax these regularity requirements and derive a much simpler and easily interpretable source condition but still achieve the same convergence rates as the standard Tikhonov regularization theory does.