I have found my problem. A boundary condition in my mesh was ill-defined 
and this lead to my error.
Sorry for the confusion.

On Monday, 19 February 2018 13:41:35 UTC-5, Bruno Blais wrote:
> Hello,
> Sorry I feel I have not explained myself correctly. Here is a drawing of 
> the case:
> <https://lh3.googleusercontent.com/-4py-EISXcqc/WosZebbKS-I/AAAAAAAAC5w/-qHRMSkwW6IinnVGocwlonnFHrF3rXXbQCLcBGAs/s1600/text4174-2.png>
> With Ux may be a profile or a constant.
> Initially I had set-up that case with Ux as a Poiseuille flow profile and 
> the Top and Bottom as no slip boundary conditions. In that case I got the 
> solution I was expecting. Convergence was good and the solution was what I 
> had in mind.
> Then what I wish to do is set Ux as a constant and apply slip at the top 
> and bottom boundary conditions. When I do this is when I am unable to reach 
> convergence in my iterative solution, yet I do not understand why because 
> the problem should be well posed.
> I don't think that leaving my right boundary as a free traction boundary 
> condition is problematic since it is by all mean an outlet boundary. This 
> worked well for instance in a backward facing step case.
> Thank you for your time, sorry for the confusion.
> Best regards
> On Monday, 19 February 2018 10:50:48 UTC-5, Timo Heister wrote:
>> > Does the order in which I apply the nonzero and zero constraints 
>> matter? 
>> These are two independent objects, so no. 
>> > Currently I apply the inlet and then the no-slip in the 
>> nonzero_constraints, 
>> > thus the bottom and top wall appear after the inlet. Afterward the 
>> cylinder 
>> > is put in the zero constraints. 
>> I don't understand. You need boundary conditions in 
>> nonzero_constraints and zero_constraints for all boundaries. The 
>> reason for these two sets is that one is used for the initial solve, 
>> while the second one is used for the Newton updates. 
>> -- 
>> Timo Heister 
>> http://www.math.clemson.edu/~heister/ 

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