Green's theorem

From Glossary of Meteorology
Revision as of 17:05, 25 April 2012 by imported>Perlwikibot
(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.


Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.