  Hard processes in diffractive deep-inelastic scattering can be described by a
factorisation into parton-level subprocesses and diffractive parton
distributions. In this framework, cross sections for inclusive dijet production
in diffractive deep-inelastic electron-proton scattering (DIS) are computed to
next-to-next-to-leading order (NNLO) QCD accuracy and compared to a
comprehensive selection of data. Predictions for the total cross sections, 39
single-differential and four double-differential distributions for six
measurements at HERA by the H1 and ZEUS collaborations are calculated. In the
studied kinematical range, the NNLO corrections are found to be sizeable and
positive. The NNLO predictions typically exceed the data, while the kinematical
shape of the data is described better at NNLO than at next-to-leading order
(NLO). A significant reduction of the scale uncertainty is achieved in
comparison to NLO predictions. Our results use the currently available NLO
diffractive parton distributions, and the discrepancy in normalisation
highlights the need for a consistent determination of these distributions at
NNLO accuracy.
