ABSTRACT
In this chapter, a method for assessing the quality of an error estimator and improving it has been presented. The originality of the analysis is to use a randomized error function in order to a priori evaluate the average behavior of the estimator. The effectivity index, that is, the ratio between the estimated and the actual error, and its asymptotic behavior are the main tools in the analysis of error estimators. The theoretical analysis of the error estimators usually finds lower and upper bounds of the global effectivity index depending on unknown constants. The error estimator composed by two computational phases, the interior projection and the patch projection. The chapter shows a numerical example coming from the error estimation procedure. The application to a simple example of error estimation in a bidimensional Poisson equation with analytical solution shows that this theory can be used in both the analysis and the practical use of the error estimator.
