A posteriori error estimation for nonlinear variational problems by duality theory

In this paper, we use the duality theory of the calculus of variations to derive a posteriori error estimates. We obtain a general form of this (duality) error estimate and show that the known classes of a posteriori error estimates are its particular cases. Bibliography: 21 titles. Dedicated to the memory of A. P. Oskolkov Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 243, 1997, pp. 201–214. Translated by S. I. Repin.