First, I'd like to point out that your question seems a bit off - IMHO.
In most FEA packages you'd set the boundary conditions (ie. how the nodes are allowed to translate/rotate and the forces) and then solve for the displacement/internal reactions. What I'm trying to say, is that your question would make sense, if you were trying to build a new solver for a specific type of problem.
That aside, the way you specified the problem, there is no one-correct answer here. For example, the following reaction model would be more appropriate if there were a slight clearance and the rod had infinite stiffness (i.e. it would rotate not bend):
The following reaction model would be more appropriate if you had the rod inside a wall that was not rigid (i.e. if the wall was allowed to deform).
The third option (at least IMHO) is the most unrealistic (I can't really think of a case where it would be really appropriate).