On 5/24/21 5:36 AM, [email protected] wrote:
I wasn't able to figure out the ordering of polynomials stored
in FE_DGQLegendre<3>. If I am correct, this class is constructed by FE_Poly's
constructor using TensorProductPolynomials of Polynomials::Legendre. If this
is indeed so, then I wasn't able to find the ordering mentioned in
TensorProductPolynomials as well.
So, like always, is the ordering lexicographic (since these are tensor product
basis functions)? Or is it based on the order of basis function (say, lowest
to highest)?
Vachan,
I don't know, but here is the way to find out assuming that you are interested
in the local enumeration (i.e., the order of shape functions within a single
cell): You create such a finite element and then output the values of the i'th
shape function via
FiniteElement::shape_value(i,p)
on a regular grid of points on the reference cell [0,1]^d.
Alternatively: For DG elements, the local enumeration equals the global
enumeration. You can generate a mesh with one cell, associated a DoFHandler
with it, and then use DataOut::build_patches() with a relatively large number
of subdivisions to output the finite element field associated with a solution
vector that has only one entry (i.e., a unit vector). This is how the pictures
of the shape functions that are shown in several of the finite element
documentation pages are generated.
Of course, if you learn how the shape functions are numbered, it would be most
excellent if you could write a short patch that adds this piece of information
to the documentation!
Best
Wolfgang
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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