Error identities for the reaction-convection-diffusion problem and applications to a posteriori error control

摘要

The paper is devoted to a posteriori error identities for the stationary reaction-convection-diffusion problem with mixed Dirichlet-Neumann boundary conditions. They reflect the most general relations between deviations of approximations from the exact solutions and those values that can be observed in a numerical experiment. The identities contain no mesh dependent constants and are valid for any function in the admissible (energy) class. Therefore, the identities and the estimates that follow from them generate universal and fully reliable tools of a posteriori error control.