`reference`

Reference elements and affine maps

Reference-element and affine-mapping helpers for teaching examples.

`ReferenceIntervalP1`

Reference linear interval element on [0, 1]. Two nodes at endpoints. Provides shape functions N₁ = 1 - ξ, N₂ = ξ and their constant derivatives. This is the 1D counterpart to ReferenceTriangleP1 for consistency.

`ReferenceTriangleP1`

Reference P1 triangle with vertices at (0,0), (1,0), (0,1). Provides barycentric shape functions N₁ = 1-ξ-η, N₂ = ξ, N₃ = η and their constant gradients.

`ReferenceQuadrilateralQ1`

Reference bilinear quadrilateral on [-1,1]². Four nodes at corners, bilinear shape functions.

`ReferenceQuadrilateralQ2`

Reference biquadratic quadrilateral on [-1,1]². Nine nodes (corners + edges + center), tensor-product Lagrange shape functions.

`ReferenceHexahedronQ1`

Reference trilinear hexahedron on [-1,1]³. Eight corner nodes, trilinear shape functions.

`ReferenceTetrahedronP1`

Reference linear tetrahedron with vertices at (0,0,0), (1,0,0), (0,1,0), (0,0,1). Barycentric shape functions.

`ReferenceTetrahedronP2`

Reference quadratic tetrahedron with 10 nodes. Second-order barycentric shape functions.

`AffineTriangleMap2D`

Affine mapping from the reference triangle to a physical triangle defined by vertices (x₁,y₁), (x₂,y₂), (x₃,y₃). Provides the Jacobian matrix J, its determinant, the inverse transpose J^{-T} for gradient pullback, and the coordinate mapping formulas.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`exact_domain(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`nodes(self)`

No docstring.

`shape_functions(self)`

No docstring.

`shape_gradients_reference(self)`

No docstring.

`jacobian(self)`

No docstring.

`det_jacobian(self)`

No docstring.

`area(self)`

No docstring.

`inverse_transpose_jacobian(self)`

No docstring.

`x_map(self)`

No docstring.

`y_map(self)`

No docstring.