I am a PhD student working in the field of numerical simulation. In several papers, the term "De Rham map" pops up (for instance in the very good thesis by Jérôme Bonelle : https://tel.archives-ouvertes.fr/tel-01116527v2/document ).
I am unsure about the definition of this term. I have come to believe that this term generally means "operation that have continuous objects correspond to discrete ones" i.e. "means of defining the actual values of the degrees of freedom of a discrete object from a continuous object", but I gradually suspect that it might rather mean "result of the integration of a cochain on a differentiable manifold". Of course, the two notions coincide in the litterature I have come accross.
So my question is : What is the definition of the term "De Rham map" ?
Regards,