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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 f_{1} and f_{2} are two scalar fields given at each point of a three-dimensional domain V limited by a closed surface S
where d Note 1 to entry: The second Green formula is symmetric with respect to | ||

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: |

** **$\underset{\text{V}}{\iiint}\left({f}_{1}\text{\hspace{0.05em}}\Delta \text{\hspace{0.05em}}{f}_{2}-{f}_{2}\text{\hspace{0.05em}}\Delta \text{\hspace{0.05em}}{f}_{1}\right)}dV={\displaystyle \underset{\text{S}}{\u222f}\left({f}_{1}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{2}-{f}_{2}\text{\hspace{0.17em}}\mathrm{grad}\text{\hspace{0.17em}}{f}_{1}\right)}\cdot {e}_{\text{n}}dA$

where d*V* is the volume element, *e*_{n}d*A* is the vector surface element and Δ is the Laplacian operator

Note 1 to entry: The second Green formula is symmetric with respect to *f*_{1} and *f*_{2}.