Hello Johannes,
As I understand it at the moment, for FEM functions are represented as a
sum of basis functions multiplied by coefficients. These basis functions
have a compact support, which is (for the case of FE_Q) one or more
cells in the triangulation, depending whether the corresponding dof sits
on a vertex, a face or a cell. The basis functions are in some way
ordered and numbered by a index. When I wrote "value of a dof", I wanted
to refer to the coefficient of the corresponding basis function (which
is the integral of the shape function when I want to represent the
constant function 1), not its index.
No, this is wrong. For simple Lagrangian elements the degrees of
freedom, and thus the coefficients you are looking for, are defined as
the point evaluation of the function (in your case the constant function
1) at the support point of the dof.
Best Regards,
Markus
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