fe_spaces

FE interpolation helpers

Finite-element interpolation helpers.

LinearElement1D

A two-node linear (P1) finite element on an interval [x0, x1]. Provides symbolic shape functions N₁ = (x₁ - x) / L and N₂ = (x - x₀) / L where L = x₁ - x₀.

local_trial_expansion(shape_functions, dofs)

Build the local trial field expansion u_h = Σ Nᵢ dᵢ. Parameters: shape_functions - tuple of shape function expressions, dofs - list of DOF symbols. Returns the expanded polynomial.

local_test_expansion(shape_functions, dofs)

Build the local test field expansion v_h = Σ Nᵢ wᵢ. Identical to local_trial_expansion (Galerkin method uses the same basis for trial and test).

length(self)

No docstring.

shape_functions(self)

No docstring.