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?
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 $\Gamma_p=\cup{ \Gamma_{pi}}$
For Finite Element formulation for fluid flow, it is sufficient to impose zero-pressure on one of the nodes.
Usually, this node is chosen on the outflow boundary. If the outflow boundary does not exist, then pick a node far away from the region(s) of steep pressure gradients.