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+---
+name: fem-formulation-spec
+description: Use when an approved structural FEM feature needs an implementation-ready mathematical formulation before numerical review or coding.
+---
+
+# FEM Formulation Specification
+
+Translate approved requirements and research into a complete mathematical contract, independent of programming APIs and storage formats.
+
+## Inputs
+
+- `docs/<feature-id>/requirements.md`
+- `docs/<feature-id>/research.md`
+- Governing standards and approved analysis assumptions
+
+## Workflow
+
+1. Fix primary variables, degrees of freedom, units, coordinates, signs, configuration, and boundary-condition conventions.
+2. Derive governing strong and weak forms with all natural and essential boundary terms.
+3. Define discretization, interpolation, kinematics, constitutive update contract, element residual/internal and external forces, and consistent tangent or stiffness.
+4. Define mapping, Jacobian validity, quadrature, state/history evolution, constraints, and result recovery that apply to the selected analysis family.
+5. State dimensions, invariants, algorithm pseudocode, numerical risks, and tests capable of falsifying each derivation.
+
+Read [analysis-family guidance](references/analysis-families.md) and apply only the sections selected by the requirements. Use [workflow and decision authority](../fem-requirements-baseline/references/workflow-and-decisions.md) for unresolved physics choices and [evidence and handoff](../fem-requirements-baseline/references/evidence-and-handoff.md) for return data.
+
+## Output
+
+Follow [Feature document management](../../../docs/FEATURE_DOCUMENTATION.md): read the Coordinator's
+feature context, keep main reports concise, and link necessary owned details in the same feature folder.
+
+Create or revise `docs/<feature-id>/formulation.md` with assumptions; variables; strong/weak forms; discretization; kinematics; constitutive contract; element equations; integration; algorithms; recovery; numerical risks; verification implications; and handoff.
+
+## Evidence
+
+Every equation defines symbols, dimensions, configuration, sign, coordinate basis, and source or derivation. Show linearization when a consistent tangent is required. Link risks and checks to requirement IDs.
+
+## Boundary
+
+Do not design source-level APIs, parsers, storage schemas, or implementation tasks. Do not silently choose physics, stabilization, interpolation, constitutive behavior, or solver semantics outside the approved contract; return that critical choice for decision.