I would like to render this surface smooth like a natural curve but don't know how I can geometriccaly transform the mesh. Thanks for your help. Maybe I could add one edge between each segment but I don't know how to do that geometrically.
You could add a loop cut in-between each of that triangular faces.
You can do that by selecting these 3 edges and subdividing them.
Select the new vertices on the corner edge and the vertices on the triangle at the bottom. Press J.
Afterwards, remove the original edges
The subsurf modifier will work much better now!