Dear all,
I am solving a problem in 2d using FE_Q(2) elements and a gauss quadrature
rule with (fe.degree +1) quadrature points in each co-ordinate direction,
that is, I have in total nine quadrature points. My question pertains to
the following:
At each cell, I need to approximate a field whose sampling (support) points
are the quadrature points belonging to reduced integration, i.e, there are
four quadrature points in my case and the four (shape) functions
approximating my field should be designed as follows:
N_j (xi_k) = delta_{jk} ,
where xi_k are the coordinates of the quadrature points. So I need four
(shape) functions, each of which is one at one of the four quadrature
points and zero at the three others.
That said, my ansatz is given by (the coefficents a(xi) are of course known)
f(xi) = a(xi_1) N_1(xi) + a(xi_2) N_2(xi) + a(xi_3) N_3(xi) + a(xi_4) N(xi)
and I need to evaluate the function f(xi) at the *nine* quadrature points.
What is the best way to do set up the FEValues object?
I have seen that there is a constructor for the FE_Q element which takes a
Quadratute<1> object. I guess this would help me to define the (shape)
functions pertaining to the field f(xi), but I think I can not evaluate
this field at the nine quadrature points, because (i) their local
coordinates are of course different in the new FEValues object and (ii)
second, I would have to insert negative local coordinates for a set of
them.
Maybe I do not even need a FEValues object for my purpuse. As I said, I
only need to do the approximation f(xi) and evaluate it at the nine
quadrature points.
Any input is greatly appreciated!
Best
Simon
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