Sorry I didn't explain myself properly. On the other hand I have a better 
understanding on the problem now. 

Long short story: Instead of setting the initial temperature to 0 as in 
most of the examples, I set it to 1. When I tried to solve the system I saw 
the artifact that I showed in the previous picture. The program was 
reporting that I had in-homogeneous boundary conditions, that's why I 
titled my question like that. But I am now sure that every quadrature point 
in the system is set to 1 and yet when solving the first step I still have 
a smaller value that appears in the adjacent points to the boundary. I 
created a minimally refined lattice and the error persists.

Le mercredi 26 juin 2024 à 18:51:55 UTC+3, Wolfgang Bangerth a écrit :

>
> Tomas,
> I must admit that I don't understand what the issue is. What does the 
> image show, and what is it you expect it to show? Part of my confusion 
> is that you use terms initial conditions, right hand side, and (in the 
> Subject line) constraints, but these are not obviously related to each 
> other.
>
> It is, of course, possible that step-32 has a bug that prevents it from 
> dealing correctly with non-zero initial conditions but that doesn't show 
> up with the zero initial conditions used there.
>
> Best
> W.
>
> On 6/26/24 07:32, Tomas Fernandez Bouvier wrote:
> > *** Caution: EXTERNAL Sender ***
> > 
> > EDIT:
> > 
> > I fixed the problem that involved inhomogeneous constraints (i had not 
> > initialized the bc matrix). However I am still struggling since boundary 
> > conditions are only being interpolated on the external face of my 
> > boundary cells.
> > 
> > 
> > Le mercredi 26 juin 2024 à 14:00:46 UTC+3, Tomas Fernandez Bouvier a 
> écrit :
> > 
> > In the context of a parallel implementation of step-26, where I
> > inspired myself in step-32, I am trying to set a different constant
> > in the initial and boundary conditions that I apply to my system.
> > Below is an image of the result when I set the initial system to 1
> > instead of 0. I tried to investigate the implementation of a rhs.
> > Somehow the conditions appear to be inhomogeneous and therefore the
> > rhs is modified. The only improvement that I got was when I muted
> > this lines in my code:
> > 
> >             if (constraints.is_inhomogeneously_constrained(
> >                   data.local_dof_indices[i]))
> >               {
> >                 for (unsigned int j = 0; j < dofs_per_cell; ++j)
> >                   data.matrix_for_bc(j, i) +=0 ;
> >                   /*
> >                     (scratch.phi_T[i] * scratch.phi_T[j] *
> >                        (use_bdf2_scheme ? ((2 * time_step +
> > old_time_step) /
> >                                            (time_step +
> > old_time_step)) :
> >                                           1.) ) *
> >                     scratch.fe_values.JxW(q);
> >                   */
> >               }
> > 
> > but I am still not able to set the entire system initial temperature
> > to 1 or any other initial value.
> > 
> > Can you help me?
> > 
> > Thank you!
> > 
> > 
> > 
> > Screenshot from 2024-06-26 13-55-07.png
> > 
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