[Getfem-users] Math behind product of three variables in high-level generic assembly

[Jan Wróblewski]

Hello everyone,

I am interested in the math behind computing a part of high-level generic
assembly term “f*u*Test_u”, where u is the FEM variable and f is initialized
fem data on the same mesh.
How is the matrix assembled in this case?
Why are there multiple iterations (at least multiple "Trace 2 in
getfem_models.cc, line 2607: Global generic assembly")?
Is creating of the matrix done by using the selected integration method to
compute integral of f*b1*b2 (where b1 and b2 are appropriate base functions
from the FEM space)?
And, most importantly, if selected integration method is good enough and FEM
space is classical 2nd order polynomials, is 2nd order of precision still
achieved?

I look forward to your responses,

Jan Wroblewski