OpenFOAM guide/Gauss' theorem

The divergence theorem relates surface and volume integrals for vectors:

$( \iint\limits_S ) \mathbf{A} \bullet \mathbf{dS} \equiv ( \iiint\limits_V ) \left ( \boldsymbol \nabla \bullet \mathbf{A} \right ) dV$
Due to notational limits with LaTeX, the brackets enclosing integrals are actually those integrals with a closed circle superposed on them

See also:

• Stoke's theorem
• gradient theorem