Alex,

have a look at step-1 
<https://www.dealii.org/8.5.0/doxygen/deal.II/step_1.html#Results>. The 
relevant piece of code there looks like

Triangulation<2>::active_cell_iterator 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classTriaActiveIterator.html> 
cell = triangulation.begin_active 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classTriangulation.html#abef8795e729458954fd7301214012665>
();
Triangulation<2>::active_cell_iterator 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classTriaActiveIterator.html> 
endc = triangulation.end 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classTriangulation.html#a55aebb671467ea1367153f81463855ca>
();
for (; cell!=endc; ++cell)
{
  for (unsigned int v=0; v < GeometryInfo<2>::vertices_per_cell; ++v)
  {
    const double distance_from_center = center.distance 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classPoint.html#a7723498de9ec90785b058a3f3c6712d2>
 
(cell->vertex(v));
    if (std::fabs(distance_from_center - inner_radius) < 1e-10)
    {
      cell->set_refine_flag ();
      break;
    }
  }
}
triangulation.execute_coarsening_and_refinement 
<https://www.dealii.org/8.5.0/doxygen/deal.II/classTriangulation.html#ac8b4fbb207303ec7f5ef758821ecd8cb>
 
();

For your purpose, it should be sufficient to check for cell->at_boundary().

Best,
Daniel

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