What nodal set is Fenics using?

mathematics
1

An important part of a FEM solver is choosing a nodal set that avoids Runge’s phenomenon. In Hesthaven and Warburton’s book “Nodal Discontinuous Galerkin Methods”, they use warp and blend points to find a nodal distribution that attempts to minimize the lebesque constant.

My question is, what nodal distribution is used in Fenics? I’m having trouble finding this information. In the book it states that “we hope to expand the collection of quadrature rules and provide more
advanced point distributions, such as Warburton’s warp-blend points”, but I don’t see where it is stated what point distributions are actually used.

Thank you!

2

You can define your quadrature rule as you like via Basix. E.g. Creating and using a quadrature rule — Basix 0.8.0.0 documentation and also using it in a custom element: Creating a custom element — Basix 0.8.0.0 documentation

@mscroggs can give more details if necessary.

3

Thank you very much. This pointed me in the direction I needed to go. I really appreciate it.

4

See in particular:
https://docs.fenicsproject.org/dolfinx/v0.7.3/python/demos/demo_lagrange_variants.html