A posteriori error estimates for approximate solutions of irregular operator equations

摘要

A scheme is proposed for deriving a posteriori error estimates and is applicable to the irregular case and is based on fairly visual minimal a priori assumptions. A mathematical model is used that has the form of the operator nonlinear equation acting from a linear normed space to an another space that does not necessarily coincide with the previous space. From a priori considerations, a projector is found and a smoothness assumption is considered. It is found that the a posteriori error estimate holds if a priori assumptions and some condition are satisfied. The results also show that the error in the approximate solution satisfies a posteriori estimate.