Fekete or Lobatto points

Question

I am working with high order FEM using polynomial CG of degree 3 or higher. I am interested on the following: In the current implementation, the nodes of CG3 (for example) are located on equally divided distances (assume the reference triangle) between each neighbours. I would like to change the location of the nodes to Fekete or Lobatto points of the triangle. Is it possible? If yes, where should look for that?

Thank you,
Murtazo

Comments

I agree with you. That would be a very useful feature for me too.
I actually submitted an enhancement request on FIAT to that regard (https://bitbucket.org/fenics-project/fiat/issues/14/gauss-legendre-lobatto-points-used-for-the); although I'm not 100% sure this is the right place..... If you feel it's worth it, you can go vote for that issue and hope that it gets enough attention.

Answer 1

You can merely tweak quadrature scheme.

To change definition of DOFs of a particular function space, you can implement a new element in FIAT and tweak FFC, UFL and DOLFIN to be aware of this element.

Comments

I have implemented Gauss-Lobatto quadrature rule in FIAT, but I now need to move the FE nodes or DOFs as you say, that seems to be not so straight forward.

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Actually, do you really need to move DOFs? The DOLFIN/UFC evaluation/quadrature mechanism is a little bit tricky but it works sufficiently. Simply said, the quadrature can be exact even if DOF nodes and quadrature nodes differ.

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I agree. It seems the spectral radius of a matrix that I am having in my problem is small when the Fekette points are used, also the Lebesgue constant of the interpolation is minimized when these points are used.