A posteriori error analysis for unstable models

In this paper, we consider the possibility of a posteriori error estimates for linear and nonlinear ill-posed operator equations. Given an auxiliary finite-dimensional problem Phi(w) = 0, Phi : D-Phi subset of E-N -> E-M that approximates the original infinite model F(x) = 0, F : D-F subset of X -> Y with a certain level of accuracy, we try to estimate the distance between z, an approximate solution to Phi(w) = 0, and x*, the exact solution to F(x) = 0. The problem Phi(w) = 0 is assumed to accumulate different sources of error (discretization, measurements, etc.), and the computed solution z is assumed to satisfy the equation Phi(w) = 0 within a nonzero tolerance delta. We conduct both a theoretical and numerical study of a posteriori error analysis.