Estimation of discontinuous elliptic coefficients

摘要

The regularized output least squares estimation technique is considered as a procedure to detect regions in which material properties are markedly different than those in the surrounding area. The problem of estimating the elliptic coefficient is studied in detail. Conditions for the uniqueness and sensitivity with respect to data of optimal interior estimators are established for finite element approximating problems. Having detected a discontinuous region, an algorithm is presented to isolate the region by alternately applying the regularized output least squares technique and a method that explicitly searches for a discontinuous parameter function.