IEVref:102-05-33ID:
Language:enStatus: Obsolete
Term: second Green formula
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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 The second Green formula is sometimes called in English “second Green theorem” or “second Green identity”.

NOTE 2 The second Green formula is symmetric with respect to f1 and f2.


Publication date:2007-08
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Internal notes:2017-06-02: Cleanup - Remove Attached Image 102-05-33en.gif
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