I define the FE space P1edge on the Coarse mesh (mesh done only with the red edges) TH.
I define the FE space P1 on the Fine mesh (all edges/vertices) Th. The boundary edges are labelled 3.

Then I compute the stiffness matrix using these two spaces.

I don’t understand why for example the second term in the first line (the term A(1,2) is nul and same for the lines 4 and 10), since each DoF of Vh located on the boundary edges should interact with the two DoF of VH, as is in the second line, I suppose.

Could someone, explain me (detailed me) the calculation that it is done ?
I can interpret the case in which I use P0edge but not the case in which I use P1edge.

I want to multiply v in Vh by a linear polynomial that is defined on the edge of the coarse mesh TH.
I have some difficulties to interpret the results.

Could you explain me (detailed me) the calculation that it is done ?
For a given Edge E in TH, is all the DoF of Vh multiplied by the same polynomial ?

Thank you for your message. I understand better the calculation that is done.

One last thing:

You use the quadrature formulae qfpE (3 points of interpolations) but you give only two of them (1±√1/3)/2. I think the last one is 0.5, isn’t it ?

“The P1edge are orthogonal polynomial of edge such that le sum is 1”: it seems that for a given edge this couple is not unique. Do you know their explicit expression ?

You put you 6 points on vertical edge
this point a the gauss point on each sub edge => exact integration for P3 polynom.

on each edge of size 1/3 4 function
first classical P1 on edge l2=x, l1=1-x on 0,1 big edge
second = f1, f2 function on gauss point (1±√1/3)/2. small edge

It is you job to do the computation but freefem++ make no error!