On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems

Karatson and Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type, see J. Karatson, S. Korotov (2009). The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the technical and numerical aspects and on the components of the error estimation, especially on the adequate solution of the involved auxiliary problem