Functional A Posteriori Error Control for Conforming Mixed Approximations of the Reaction-Convection-Diffusion Problem
Provides theoretical error bounds for numerical approximations in computational fluid dynamics, but is incremental as it extends existing functional error control to a specific problem class.
The paper derives exact global error values for conforming mixed approximations of the reaction-convection-diffusion problem using functional a posteriori error control, with error equalities under isometry conditions and two-sided estimates otherwise.
In this paper we show how to obtain the exact value of the global error of a conforming mixed approximation of the reaction-convection-diffusion problem. We operate in the framework of functional type a posteriori error control. The error is measured in a combined norm which takes into account both the primal and dual variables. Our main results state that the exact global error value of a conforming mixed approximation is given by a functional which includes only known quantities. The presented error equalities hold with certain restrictions on the reaction coefficient and the convection vector, namely, under the conditions when the solution operators of the corresponding problems are isometries. For the case where these restrictions are not satisfied we derive a two-sided error estimate.