IEVref: 102-05-33 ID: Language: en Status: Standard Term: second Green formula Synonym1: second Green theorem Synonym2: second Green identity Synonym3: Symbol: Definition: identity resulting from the divergence theorem applied to the vector field ${f}_{1}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{2}-{f}_{2}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{1}$, where f1 and f2 are two scalar fields given at each point of a three-dimensional domain V limited by a closed surface S $\underset{\text{V}}{\iiint }\left({f}_{1}\text{ }\Delta \text{ }{f}_{2}-{f}_{2}\text{ }\Delta \text{ }{f}_{1}\right)dV=\underset{\text{S}}{∯}\left({f}_{1}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{2}-{f}_{2}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{1}\right)\cdot {e}_{\text{n}}dA$ where dV is the volume element, endA is the vector surface element and Δ is the Laplacian operatorNote 1 to entry: The second Green formula is symmetric with respect to f1 and f2. Publication date: 2017-07 Source: Replaces: 102-05-33:2007-08 Internal notes: CO remarks: TC/SC remarks: VT remarks: Domain1: Domain2: Domain3: Domain4: Domain5: