High-order mixed-field interpolation

Use spaces.independent_subspace(W, component) for standalone boundary fields and output fields on a mixed space. It preserves the component finite element but creates independent degree-of-freedom numbering. Transfer values by interpolation, never by copying coefficient arrays between these spaces.

from dolfinx import fem
from agentfem import spaces

V = spaces.independent_subspace(W, 0)
g = fem.Function(V)
g.interpolate(boundary_values)
boundary_dofs = fem.locate_dofs_topological((W.sub(0), V), facet_dim, facets)
bc = fem.dirichletbc(g, boundary_dofs, W.sub(0))

velocity = fem.Function(V)
velocity.interpolate(solution.sub(0))
velocity.x.scatter_forward()

VelocityPressureUnknown.collapsed_velocity() and .collapsed_pressure() perform this physical interpolation automatically. The mixed solid unknown's corresponding methods follow the same route. Their returned fields retain the same element degree and physical value shape; coefficient ordering is not a public interchange format.

In a polygon-hole Stokes development replay, creating boundary and output fields through raw collapsed mixed spaces produced approximately 3% error with a fourth-order velocity element. Independent spaces with explicit field interpolation reduced this to 2.30e-7 relative error on the same mesh. The failure also reproduced in a local DOLFINx 0.11 environment. This observation does not establish that all collapse operations are incorrect, or that all backends share the same defect. It motivates the explicit transfer route and polynomial reproduction regressions in two and three dimensions.

The original benchmark output is preserved. This is a post-development numerical repair, not a revised first-attempt model score.