Dear Wolfgang,
This was easier than I thought. I followed your suggestion and used 
VectorTools::interpolate
Final solution to set the values of the DOF using a parsed function:

// initialConditionParameters.uvw is my parsed function
// newtonUpdate is my local vector that I use to alter the DOF values


  const FEValuesExtractors::Vector velocities (0);

  const FEValuesExtractors::Scalar pressure (dim);

  const MappingQ<dim>      mapping (degreeVelocity_,femParameters.qmapping_all);

  VectorTools::interpolate(mapping, 

                           dof_handler,

                           initialConditionParameters.uvw,

                           newton_update,

                           fe.component_mask(velocities));


Thank you very much for the help!

On Thursday, 25 April 2019 09:32:09 UTC-4, Wolfgang Bangerth wrote:
>
> On 4/25/19 6:58 AM, Bruno Blais wrote: 
> > I would like to be able to set-up an initial condition by fixing the 
> value of 
> > the DOF themselves by using their x,y(,z) position with a ParsedFuction. 
> > 
> > Generally, I set the initial condition by using an L2 projection of the 
> > function (for complex function and higher order element I know this is 
> more 
> > appropriate). 
> > However, for some stuff I would like to be able to fix the value of the 
> DOF 
> > directly. 
> > My issue is, through the doxygen, I have not found a way to loop through 
> the 
> > DOF and to extract their position, even more when I have high order 
> element or 
> > when I have a multiplicity (say velocity-vector + pressure). 
> > 
> > What I would be looking into doing would be something similar to : 
> > 
> > loop over local DOF; 
> >    get DOF position 
> >    get DOF component (u[0], u[1], u[2], p) 
> >    calculate parsed function using the point 
> >    set the value of the DOF 
> > end 
> > 
> > Is it something that is possible? This is a weird way of iterating since 
> I 
> > know we always loop over the cells. Maybe there is a way to achieve this 
> by 
> > looping over the cells and then looping over the DOF of the cells? This 
> would 
> > be slightly redundant, but I do not care since I am doing this only 
> once. 
>
> You can get the locations of DoFs using 
> DoFTools::map_dofs_to_support_points(). 
>
> But maybe the easier way is to use 
> VectorTools::interpolate_boundary_values() 
> or project() and just pass it a function object that describes the 
> function 
> you want to set in terms of (x,y,z). This could be your ParsedFunction. 
> interpolate_b_v() will then call your parsed function with a bunch of 
> points 
> that happen to correspond to the DoF locations, but it makes the 
> connection 
> internally and you no longer need to worry about which DoF sits where. 
>
> Best 
>   W. 
>
>
> -- 
> ------------------------------------------------------------------------ 
> Wolfgang Bangerth          email:                 [email protected] 
> <javascript:> 
>                             www: http://www.math.colostate.edu/~bangerth/ 
>
>

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