FEValues

GeometryMapping{DiffOrder}(::Type{T}, ip_geo, qr::QuadratureRule)

Create a GeometryMapping object which contains the geometric

• shape values
• gradient values (if DiffOrder ≥ 1)
• hessians values (if DiffOrder ≥ 2)

T<:AbstractFloat gives the numeric type of the values.

MappingValues(J, H)

The mapping values are calculated based on a geometric_mapping::GeometryMapping along with the cell coordinates, and the stored jacobian, J, and potentially hessian, H, are used when mapping the FunctionValues to the current cell during reinit!.

FunctionValues{DiffOrder}(::Type{T}, ip_fun, qr::QuadratureRule, ip_geo::VectorizedInterpolation)

Create a FunctionValues object containing the shape values and gradients (up to order DiffOrder) for both the reference cell (precalculated) and the real cell (updated in reinit!).

BCValues(func_interpol::Interpolation, geom_interpol::Interpolation, boundary_type::Union{Type{<:BoundaryIndex}})

BCValues stores the shape values at all facet/faces/edges/vertices (depending on boundary_type) for the geometric interpolation (geom_interpol), for each dof-position determined by the func_interpol. Used mainly by the ConstraintHandler.

embedding_det(J::SMatrix{3, 2})

Embedding determinant for surfaces in 3D.

TLDR: "det(J) =" ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂

The transformation theorem for some function f on a 2D surface in 3D space leads to ∫ f ⋅ dS = ∫ f ⋅ (∂x/∂ξ₁ × ∂x/∂ξ₂) dξ₁dξ₂ = ∫ f ⋅ n ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ dξ₁dξ₂ where ||∂x/∂ξ₁ × ∂x/∂ξ₂||₂ is "detJ" and n is the unit normal. See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation. For more details see e.g. the doctoral thesis by Mirza Cenanovic Tangential Calculus [12].

embedding_det(J::Union{SMatrix{2, 1}, SMatrix{3, 1}})

Embedding determinant for curves in 2D and 3D.

TLDR: "det(J) =" ||∂x/∂ξ||₂

The transformation theorem for some function f on a 1D curve in 2D and 3D space leads to ∫ f ⋅ dE = ∫ f ⋅ ∂x/∂ξ dξ = ∫ f ⋅ t ||∂x/∂ξ||₂ dξ where ||∂x/∂ξ||₂ is "detJ" and t is "the unit tangent". See e.g. https://scicomp.stackexchange.com/questions/41741/integration-of-d-1-dimensional-functions-on-finite-element-surfaces for simple explanation.

shape_value_type(fe_v::AbstractValues)

Return the type of shape_value(fe_v, q_point, base_function)

shape_gradient_type(fe_v::AbstractValues)

Return the type of shape_gradient(fe_v, q_point, base_function)

ValuesUpdateFlags(ip_fun::Interpolation; update_gradients = Val(true), update_hessians = Val(false), update_detJdV = Val(true))

Creates a singelton type for specifying what parts of the AbstractValues should be updated. Note that this is internal API used to get type-stable construction. Keyword arguments in AbstractValues constructors are forwarded, and the public API is passing these as Bool, while the ValuesUpdateFlags method supports both boolean and Val(::Bool) keyword args.