Green's theorem

From Glossary of Meteorology
Revision as of 18:10, 26 January 2012 by imported>Perlwikibot (Created page with " {{TermHeader}} {{TermSearch}} <div class="termentry"> <div class="term"> == Green's theorem == </div> <div class="definition"><div class="short_definition">A form of t...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)



Green's theorem

A form of the divergence theorem applied to a vector field so chosen as to yield a formula useful in applying the Green's function method of solution of a boundary-value problem.

The most common form of the theorem is
ams2001glos-Ge47
where dV and dS are elements of the volume V and closed bounding surface S, respectively; φ and ψ are any twice differential functions with continuous second partial derivatives in V; n is the outer normal to S; and ∇2 is the Laplacian operator.