(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled) (Untitled)(Untitled)Examples




IEVref:102-05-33ID:
Language:enStatus: 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 grad f 2 f 2 grad f 1 MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqipG0dh9qqWrVepG0dbbL8F4rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaaiaadAgadaWgaaWcba GaaGymaaqabaGccaaMc8ocbeGaa83zaiaa=jhacaWFHbGaa8hzaiaa ykW7caWGMbWaaSbaaSqaaiaaikdaaeqaaOGaeyOeI0IaamOzamaaBa aaleaacaaIYaaabeaakiaaykW7caWFNbGaa8NCaiaa=fgacaWFKbGa aGPaVlaadAgadaWgaaWcbaGaaGymaaqabaaaaa@4B1E@ , where f1 and f2 are two scalar fields given at each point of a three-dimensional domain V limited by a closed surface S

V ( f 1 Δ f 2 f 2 Δ f 1 ) dV= S ( f 1 grad f 2 f 2 grad f 1 ) e n dA MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbbjxAHX garuavP1wzZbItLDhis9wBH5garmWu51MyVXgarqqtubsr4rNCHbGe aGqk0di9Wr=fpeei0di9v8qiW7rqqrVepeea0xe9LqFf0xc9q8qqaq Fn0lXdHiVcFbIOFHK8Feea0dXdar=Jb9hs0dXdHuk9fr=xfr=xfrpe WZqaaeaaciWacmGadaGadeaabaGaaqaaaOqaamaapmfabaWaaeWaae aacaWGMbWaaSbaaSqaaKqzaeGaaGymaaWcbeaakiaayIW7imaacqWF uoarcaaMi8UaamOzamaaBaaaleaajugabiaaikdaaSqabaGccqGHsi slcaWGMbWaaSbaaSqaaKqzaeGaaGOmaaWcbeaakiaayIW7cqWFuoar caaMi8UaamOzamaaBaaaleaajugabiaaigdaaSqabaaakiaawIcaca GLPaaaaSqaaiaabAfaaeqaniabgUIiYlabgUIiYlabgUIiYdqcLbua caGGKbGccaWGwbGaeyypa0Zaa8GvaeaadaqadaqaaiaadAgadaWgaa WcbaqcLbqacaaIXaaaleqaaOGaaGPaVJqabKqzafGaa43zaiaa+jha caGFHbGaa4hzaOGaaGPaVlaadAgadaWgaaWcbaqcLbqacaaIYaaale qaaOGaeyOeI0IaamOzamaaBaaaleaajugabiaaikdaaSqabaGccaaM c8EcLbuacaGFNbGaa4NCaiaa+fgacaGFKbGccaaMc8UaamOzamaaBa aaleaajugabiaaigdaaSqabaaakiaawIcacaGLPaaaaSqaaKqzaeGa ae4uaaWcbeqdcqWIs4U0cqGHRiI8cqGHRiI8aOGaeyyXICTaaCyzam aaBaaaleaajugabiaab6gaaSqabaqcLbuacaGGKbGccaWGbbaaaa@81AA@

where dV is the volume element, endA is the vector surface element and Δ is the Laplacian operator

Note 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: