FEEC overview (lowest order)

FrontIntrinsicOps.jl now exposes a lowest-order FEEC-compatible layer on top of the existing DEC core.

This layer is additive:

• DEC operators (d0, d1, diagonal Hodge stars, existing PDE solvers) remain unchanged.
• FEEC adds Whitney spaces, canonical interpolation, and consistent variational assembly.

Discrete de Rham sequence

On triangulated surfaces:

0 -> Λh0 --d0--> Λh1 --d1--> Λh2 -> 0

with DOFs:

• Λh0: vertex values,
• Λh1: oriented edge integrals,
• Λh2: oriented face integrals.

Public entry points

• build_whitney_complex(mesh, geom)
• build_de_rham_sequence(mesh, geom)
• de_rham_report(complex)
• verify_subcomplex(complex)

Storage conventions

• 0-form cochains: Vector length nV.
• 1-form cochains: Vector length nE in canonical oriented-edge order (i<j).
• 2-form cochains: Vector length nF in face order.

Minimal example

using FrontIntrinsicOps

mesh = generate_icosphere(1.0, 2)
geom = compute_geometry(mesh)

W = build_whitney_complex(mesh, geom)
rpt = de_rham_report(W)

println(rpt.ndofs0, " ", rpt.ndofs1, " ", rpt.ndofs2)
println("d1*d0 residual = ", rpt.exactness_residuals.d1_d0)

Limitations and non-goals

• Lowest-order only (Whitney0/1/2).
• Simplicial meshes only (curves/surfaces).
• Canonical FEEC interpolators only (no smoothed bounded projectors yet).
• No higher-order P_r / P_r^- families in this round.