InteriorBasis?

When I first saw skfem.InteriorBasis, I got a little confused because I thought it doesn’t take into account the dofs on the boundary. If I understand correctly, the name is just to set it apart from FacetBasis (which if I understand correctly only means the boundary facets, right?). If this is true, I would suggest to rename InteriorBasis. How about ElementBasis or just Basis? FacetBasis could then be SurfaceBasis or BoundaryBasis or something like that.

[kinnala]

I’m also not against renaming InteriorBasis to CellBasis and adding a new alias Basis->CellBasis because CellBasis is what you usually want to use.

[kinnala]

Some of my ideas.

• What is Basis object?

A collection of finite element basis function values (and optionally gradients, second derivatives), evaluated at quadrature points.

• What about InteriorBasis or FacetBasis?

Quadrature points are associated with either elements/cells or facets. “Associated with” means that the quadrature points are used to integrate over elements/cells or over facets.

• InteriorBasis has quadrature points associated with elements/cells. In most cases these quadrature points are, in fact, interior to the mesh/domain (not touching the boundary or any interior facets) because this is preferred, e.g., when having discontinuous material fields. But this is not a hard requirement.
• FacetBasis (that is, ExteriorFacetBasis) has quadrature points associated with boundary facets.
• ExteriorFacetBasis is obviously a bad name: exterior is outside of the domain which is not the case. Hence, rename to BoundaryFacetBasis.
• ElementBasis or CellBasis are fine, but “element” has kind of dual meaning (“elements” of the mesh vs. “finite element” which refers to the combination of reference domain, polynomial order and degrees-of-freedom). Because we already have skfem.element.Element, I thought also that ElementBasis can be confusing.
• Therefore, CellBasis remains.