element -> cell in transformation functions

[KnutAM]

To be consistent with the notation in Ferrite,

• facet_to_element_transformation -> facet_to_cell_transformation
• element_to_facet_transformation -> cell_to_facet_transformation

(edited to as I mistakenly used cell on both from and to...)

Ferrite.jl/src/FEValues/face_integrals.jl

Lines 1 to 15 in b8f986a

	"""
	facet_to_element_transformation(point::Vec, ::Type{<:AbstractRefShape}, facet::Int)
	Transform quadrature point from the facet's reference coordinates to coordinates on the
	cell's facet, increasing the number of dimensions by one.
	"""
	facet_to_element_transformation
	"""
	element_to_facet_transformation(point::AbstractVector, ::Type{<:AbstractRefShape}, facet::Int)
	Transform quadrature point from the cell's coordinates to the facet's reference coordinates, decreasing the number of dimensions by one.
	This is the inverse of `facet_to_element_transformation`.
	"""
	element_to_facet_transformation

Since this is only in devdocs, I guess we can change it as a minor version change?

For the documentation, we are also mixing (discussed somewhere else before, but to keep the discussion together, pointing out here too) between cell, element, and (reference) shape. From our convention in #914, I think we ideally should have ReferenceCell and not ReferenceShape, but since AbstractReferenceShape already exists, I guess it makes sense to keep shape for the reference (cells/shapes)? However, I think removing the element from https://ferrite-fem.github.io/Ferrite.jl/dev/devdocs/elements/ would make sense.

Thoughts @termi-official, @lijas, @fredrikekre, and more?

[termi-official]

I am fine with this. We should in this turn also include a table similar to https://defelement.org/ciarlet.html#Cell+subentities somewhere (with credits to this page ofc).

Furthermore, I think we should clarify what we mean with "element" (and maybe "finite element"), since I think I introduced the work "element" into Ferrite.

[KnutAM]

We should in this turn also include a table similar to https://defelement.org/ciarlet.html#Cell+subentities somewhere (with credits to this page ofc).

We have included that information here: https://ferrite-fem.github.io/Ferrite.jl/dev/topics/reference_shapes/#Entity-naming

Furthermore, I think we should clarify what we mean with "element" (and maybe "finite element"), since I think I introduced the work "element" into Ferrite.

That sounds good to me. Can try to write something up on that when I find time unless someone beats me to it.

[termi-official]

Okay, maybe we should rename the section title. I am not sure that users will expect to find the information in htere https://ferrite-fem.github.io/Ferrite.jl/dev/topics/reference_shapes/#Entity-naming

[KnutAM]

Okay, maybe we should rename the section title.

Any suggestions?

[KnutAM]

Furthermore, I think we should clarify what we mean with "element" (and maybe "finite element"), since I think I introduced the work "element" into Ferrite.

Before doing any writing of this, the definitions that I have in my head would be something like the following. (Please give feedback)

• Cell: The geometry of one element in the mesh or grid. Described by nodal coordinates and a geometric interpolation.
• Reference shape: The reference geometry of a cell, which defines the local entity numbering. Interpolations (shape functions) are defined on this geometry, and mapped to the actual cell's geometry.
• Element: The (finite) element is described by its cell, the function interpolations of all the associated fields, the constitutive behavior(s), and the integration (typically quadrature) rule.