Description:
While implementing a new element (#12897), I needed to add Lobatto quadratures.

Currently, Lobatto quadratures exist in Kratos for some geometries, but not all, and they’re not generally usable for arbitrary orders or integrations. To address this, I added order-one Lobatto quadratures (LOBATTO_1) for the classical geometries:

• Linear triangle
• Quadrilateral
• Tetrahedron
• Hexahedron

Open Issues

Purpose of GI_GAUSS_EXTENDED:
The GI_GAUSS_EXTENDED quadratures appear inconsistent. Depending on the geometry, they either perform collocation or behave identically to standard Gauss quadratures.

• What is their intended general purpose?
• Do we actually need them, given these inconsistencies?

Handling Missing Quadrature Implementations:
As it stands, all entries of the quadrature enumeration must be filled, even for cases where specific implementations are unavailable. This leads to duplicated definitions like using Gauss quadratures for GI_EXTENDED.

• Should we adjust this requirement or provide a fallback mechanism?

Looking for feedback and suggestions on these points to improve the quadrature handling in Kratos.

@loumalouomega @rubenzorrilla @RiccardoRossi