Goal oriented adaptivity in the IRGNM for parameter identification in PDEs I:\\ reduced formulation

摘要

In this paper we study adaptive discretization of the iteratively regularizedGauss-Newton method IRGNM with an a posteriori (discrepancy principle) choiceof the regularization parameter in each Newton step and of the stopping index.We first of all prove convergence and convergence rates under some accuracyrequirements formulated in terms of four quantities of interest. Thencomputation of error estimators for these quantities based on a weighted dualresidual method is discussed, which results in an algorithm for adaptiverefinement. Finally we extend the results from the Hilbert space setting with quadraticpenalty to Banach spaces and general Tikhonov functionals for the regularization of each Newton step.