A posteriori error identities for parabolic convection–diffusion problems

In the paper, we derive and discuss integral identities that hold for the difference between the exact solution of initial-boundary value problems generated by the reaction–convection–diffusion equation and any arbitrary function from admissible (energy) class. One side of the identity forms a natural measure of the distance between the exact solution and its approximation, while the other one is either directly computable or natural measure serves as a source of fully computable error bounds. A posteriori error identities and error estimates are derived in the most general form without using special features of a function compared with the exact solution. Therefore, they are valid for a wide spectrum of approximations constructed different numerical methods and can be also used for the evaluation of modelling errors.