This is the first analysis of a benchmark star in the framework of the Gaia space mission. The focus of this paper is on methodology which must be robust and effective, as it is to be applied to a sizable number of late-type benchmark stars. We shall test this new method on stars that are, e.g., 1000\,K cooler than $\delta$ Eri. The spectrum of such stars is expected to be much more challenging to analyse due to the problems with continuum normalization and line blending. This will be the subject of future investigations.

For $\delta$ Eri, the method works well and gives good mutual confirmation for the individual abundances independently derived from optical and Gaia-RVS spectra, even in LTE. At 0.01\,dex, the abundances derived are indistinguishable within the errors and their agreement is rather satisfactory. But this result was achieved based on high-resolution spectra, while Gaia spectra will not be of the same quality.

Keeping all that in mind, our recommendations would be the following: test this methodology against a comprehensive set of benchmark stars (already scheduled for observations). This will show the possible limitations of such a data treatment. If this turns out to be a success, one can start to degrade the data quality to reflect typical Gaia-RVS data. At that stage, problems may become apparent in the form of systematic offsets in inferred quantities and the most direct approach used in high-resolution spectroscopy will no longer be applicable. This may result in the introduction of some correction factors or weights. Finally, one of the future tasks will be implementation of 3D model atmospheres and line-synthesis calculation in NLTE.
