DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Fortin operator for a discrete constraint

Definition

Let $V, Q, b$ be as in Stokes velocity and pressure spaces and weak forms, and let $V_{h} \subset V$ , $Q_{h} \subset Q$ be finite-dimensional subspaces. A Fortin operator is a bounded linear map $Π_{h} : V \to V_{h}$ for which there is a constant $C_{F}$ such that $∥ Π_{h} v ∥_{V} \leq C_{F} ∥ v ∥_{V} (v \in V), b (Π_{h} v, q_{h}) = b (v, q_{h}) (v \in V, q_{h} \in Q_{h}) .$ The second condition is exact constraint preservation. It does not assert $div Π_{h} v = div v$ pointwise.

Depends on

Stokes velocity and pressure spaces and weak forms

Used by

Dependency tree · two levels

6 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Jean-Luc Guermond, MATH 661 Fall 2025, Chapters 53–54 (complete course notes) (standard reference, not scraped)
Daniele Boffi, Franco Brezzi, Michel Fortin, Mixed Finite Element Methods and Applications (complete textbook) (standard reference, not scraped)