I'm wondering if it's possible/straightforward to have per-cell quadrature 
weights? I want to keep the quadrature positions the same but update the 
quadrature weights.

I have looked through the documentation, and in particular the elasticity 
example <https://dealii.org/developer/doxygen/deal.II/step_8.html>, and 
these lines in particular seem like a fruitful start to understanding how 
one might do this:

    FEValues<dim> fe_values (fe, quadrature_formula,
                             update_values   | update_gradients |
                             update_quadrature_points | update_JxW_values);
...

    typename DoFHandler<dim>::active_cell_iterator cell = 
dof_handler.begin_active(),
                                                   endc = dof_handler.end();
    for (; cell!=endc; ++cell)
      {
        cell_matrix = 0;
        cell_rhs = 0;
        fe_values.reinit (cell);
....

So it seems fe_values is being initialized with quadrature rule and reinited 
with each cell (as described here 
<https://www.dealii.org/8.4.1/doxygen/deal.II/group__UpdateFlags.html>). 
However, I want to reinit with a new quadrature rule as well as new 
mapping. Is this possible?

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