A posteriori error estimates for the solution of nonlinear ill-posed operator equations

In this paper we consider a posteriori estimates for inverse and ill-posed problems. A posteriori estimates are widely used in finite element methods (e.g. in two-level methods) for the solution of nonlinear partial differential equations. Such estimates are not available for ill-posed problems since usually the derivation requires well-posedness assumptions. In this paper we derive a posteriori estimates for ill-posed problems using source conditions.