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 <: AbstractValues object containing the shape values and gradients (up to order DiffOrder) for both the reference cell (precalculated) and the real cell (updated in reinit!). The user should normally not create FunctionValues, these are typically only created from the constructors of AbstractCellValues and AbstractFacetValues. However, the user will interact with fv::FunctionValues when indexing e.g. cmv::MultiFieldCellValues (e.g. fv = cmv.u), as fv supports

• getnbasefunctions
• shape_value
• shape_gradient
• shape_symmetric_gradient
• shape_divergence
• function_value
• function_gradient
• function_symmetric_gradient
• function_divergence

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 [13].

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 singleton 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.