A Posteriori Error Estimation of “Quantities of Interest” on “Quantity-Adapted” Meshes

Abstract

A posteriori error estimation plays an important role in the modern numerical analysis. The direction from which this topic initially started was the estimation of the computational error in global (energy) norm. Concerning various approaches for this type of estimation we refer to works [1], [2], [3], [4], [5], [6], [13], [15], [16], [17], [18]. For approximations of linear elliptic problems, they examine error estimates in the global (energy) norm and suggest error indicators/estimators that are further used in various mesh adaptive procedures (see, e.g., [10]). Global error estimates give a general presentation on the quality of an approximate solution and a stopping criteria.