Error Estimates for the Numerical Identification of a Variable Coefficient

Abstract

Abstract. Error estimates are derived for the approximate identification of an unknown transmissivity coefficient in a partial differential equation describing a model problem in groundwater now. The approximation scheme considered determines the coefficient by least squares fitting of the observed pressure data.

Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients

“…In this work, the coefficient q is represented by level set functions. Correspondingly, we replace the minimization of q by an updating of the constant values q kþ1 i using a gradient method as in (17) and (18) and an updating the level set functions / kþ1 j also by a gradient method as in (19) and (20). We expect that this algorithm also has a linear convergence rate at least near the true minimizer.…”

“…In the presence of noise in the observation data, it has been shown theoretically, cf. [19,20,[41][42][43], that the approximation error increases as the mesh size decreases. Up to now, it seems that there are not many available algorithms that can solve this inverse problem with relative large noise on a sufficient fine mesh.…”

Adaptive finite element methods for the identification of distributed parameters in elliptic equation

“…However, to our knowledge, there are few published results on this topic for parameter identification problems, we refer to [4,16,26] for more details.…”

Convergence rates for Tikhonov regularization of a two-coefficient identification problem in an elliptic boundary value problem

“…The last problems arise from different contexts of applied sciences, e.g., from aquifer analysis. For surveys on the subject, we refer the reader to [4,5,9,13,[16][17][18]22,26,28,31,34,35,40] and the references therein. To our knowledge, Baumeister and Kunisch [5] were the first who investigated the above inverse problem and that for the Dirichlet problem.…”