  This paper concerns quantitative analysis of errors generated by incompletely
known data in convex minimization problems. The problems are discussed in the
mixed setting and the duality gap is used as the fundamental error measure. The
influence of the indeterminate data is measured using the worst case scenario
approach. The worst case error is decomposed into two computable quantities,
which allows the quantitative comparison between errors resulting from the
inaccuracy of the approximation and the data uncertainty. The proposed approach
is demonstrated on a paradigm of a nonlinear reaction-diffusion problem
together with numerical examples.
