Dear deal.II community,

I have a problem where some of my data are discontinuous and such that it 
is not resolved by the triangulation. Let's say I have an element K and I 
want to integrate a function f that has a discontinuity in K. The 
discontinuity of f divides K into two parts, K1 and K2. Obviously a global 
quadrature rule over the whole cell would not be a good option, and I am 
not willing to refine my cell in order to have the discontinuity along the 
element edge. Instead I would like to split the integral into two parts, 
one over K1 and one over K2, then apply quadrature to each of them, and 
finally sum the contributions. 

The QIterated class provides some features in this direction, but is not 
flexible enough since it divides the quadrature into equally spaced 
intervals. I could try to not use FEValues and work directly with the 
Quadrature class, but then I also need a mapping to the reference cell and 
the Mapping classes seems to depend on mapping from a cell, not just a 
portion of a cell.

Have anyone considered such problems before in the deal.II framework? If 
not, I would be happy for any hints towards how I can resolve this issue.

Kind regards,
Lars Hov Odsæter

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