An Elementary method of Deriving A Posteriori Error Equalities and Estimates for Linear Partial Differential Equations

In this paper we present a simple method of deriving a posteriori error equalities and estimates for linear elliptic and parabolic partial differential equations. The error is measured in a combined norm taking into account both the primal and dual variables. We work only on the continuous (often called functional) level and do not suppose any specific properties of numerical methods and discretizations.