# Partial integration in 2D - Green's Theorem

• Nov 5th 2009, 04:58 AM
jeneverboy
Partial integration in 2D - Green's Theorem
Hi

Using Green's Theorem:

$\int_{\Omega} c div \mathbf{u} d \Omega = - \int_{\Omega} (grad \; c) \cdot \mathbf{u} d \Omega + \oint_{\Gamma} c \mathbf{u} \cdot \mathbf{n} d \Gamma$

One can write a partial integration in 2D:

$\int_{\Omega} c \frac{\partial v}{\partial y} \frac{\partial \phi}{\partial x} d \Omega = - \int_{\Omega} c \frac{\partial v}{\partial y} \frac{\partial }{\partial x} \phi d \Omega + \oint_{\Gamma} c \phi \frac{\partial v}{\partial y} n_{1} d \Gamma$

My question: Is the integral-term on $\Gamma$ zero because the normal $n_{1}$ is in x-direction and $\frac{\partial v}{\partial y}$ in y-direction? Or should it be:
$\int_{\Gamma} c \phi \frac{\partial v}{\partial y} d \Gamma$

My first question here, I hope somebody can help me.

Alex.