# Imposing total pressure over surface in FEM

I am trying to solve Stokes problem using Finite element method.

My question is how to impose that total pressure over the surface is zero to remove the constant pressure mode?

You must add an additional equation to your system. It is: $$\int_{\Gamma_p}{p\,d\sigma}=0\implies \sum_{p_i\in \Gamma_p}p_i\int_{\Gamma_{pi}}{\phi(t)\,dt}=0$$
Where $\phi(t)$ is the basis function of $p$ along the parameterised boundary described with the parameter $t$ in the element $\Gamma_{pi}$. Remember that $\Gamma_p=\cup{ \Gamma_{pi}}$