Stokes flow unique pressure solution

Hi,

I’m struggling to get a unique pressure solution when solving the Stokes equations on a ‘homemade’ mesh. When integrating the pressure terms and applying stress conditions inc surface tension within the variational formulation the solution comes out incorrect. I know that the velocity solution should be given by u = 0, since this is how I derived the shape of the mesh in the first place which I’m now trying to verify.

I’ve seen on other forum posts that I could define a point wise Dirichlet condition or a penalty condition but both of these don’t work. There must be a standard way to get the correct solution without penalising the pressure to zero everywhere?

Thanks

Thanks