Thanks Bruno.
By Vertex, I meant the geometric quantity only. As I have used first order 
scalar basis functions i.e FE_Q<2> fe(1) to distribute the degrees of 
freedom by dof_handler.distribute_dofs(fe);. I expect 'n_dofs = n_vertices' 
and also the finite element nodes to be residing directly on the geometric 
vertices.  So when I use  'vertices = triangulation.get_vertices();' I 
expect the number of elements(Points) in vertices array to be equal to the 
number of nodes(geometric vertices) in my mesh. Also I expected these 
elements (Points of vertices array) to be sorted(indexed) in the increasing 
order of its global_dof_index (which is assigned by 
'dof_handler.distribute_dofs(fe)' ). So I used 'Point<2> point1 = 
vertices[local_dof_indices[i]];' to fetch the geometric vertex from the 
array, pick the x-coordinate and assign it as scalar solution at that 
vertex/node. I am doing all this as I have to solve a moving domain problem 
in the future.
I have accomplished this by the following code, but I am looking for more 
efficient ways and better understand dealii.
      for (; cell!=endc; ++cell)
    {
    cell->get_dof_indices(local_dof_indices);
    for (int v=0; v<dofs_per_cell; ++v)
  {
    point1  = (cell->vertex(v));
    solution(local_dof_indices[v]) = point1(0);
  }
    }  

<https://lh3.googleusercontent.com/-8Tou3ImtV2Q/WRVjhNHXWgI/AAAAAAAABtw/gJ5T7gbf2NgsM-QBQjzzuiL95uXdxICZgCLcB/s1600/Screenshot_20170512_130049.png>
Please suggest. Please correct if my understanding is wrong.

Thanks,
Bhanu

On Friday, May 12, 2017 at 1:03:12 AM UTC+5:30, Bruno Turcksin wrote:
>
> Bhanu,
>
> On Thursday, May 11, 2017 at 3:03:03 PM UTC-4, Bhanu Teja wrote:
>
>> What is the order these vertices are placed in the vector(does it 
>> correspond to the node/vertex number/index as defined by the dof_handler?)?
>>
>> I think you misundertand what is a vertex in deal.II A vertex is only a 
> geometric quantity that has nothing to do with your finite element space. 
> There are not related to degrees of freedom.  I think that the interpolate 
> function 
> http://dealii.org/8.5.0/doxygen/deal.II/namespaceVectorTools.html#a0d267850685f04deb2943076b3640b4f
>  
> does what you want.
>
> Best,
>
> Bruno
>

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