# Tag Info

Accepted

### Boundary condition for Pressure in Navier-Stokes equation

When we say that the pressure is only defined "up to a constant", what we mean is this: If $u,p$ is a solution to the Navier-Stokes equations, then $u,p+c$ for any constant $c$ is also a solution. In ...
• 55.7k

### Why can the weak forms of the Stokes and continuity equations be combined into a single equation?

To get from weak form I to II, just add the two equations of weak form I. To see the other direction, note that weak form II has to hold for all test functions $\phi$ and $\psi$. That is, you can test ...
• 451

### Has a uniform estimate in k of the inf-sup constant for hp-DG methods for the Stokes problem been established?

The problem was solved recently: Lederer/Schöberl: Polynomial robust stability analysis for H(div)-conforming finite elements for the Stokes equations
• 1,124

### Incompressible Navier-Stokes equations: Is projection method exact?

Note: I originally posted an answer that I was not 100% pleased with, so I have revised it heavily. 1/20/2017 The projection method is not in an exact approximation to the full system in general. ...
• 71

### How can I make sure the flow is divergence-free when I use moving mesh?

It's important to realize that the original velocity field $\mathbf v_0$ is also not divergence free in a pointwise sense. Rather, it is only divergence free when tested with the pressure test ...
• 55.7k
Accepted

### Can we simulate incompressible flows using the (slight) density changes to give pressure?

Water (and other fluids that are considered incompressible) are of course in reality compressible -- just not very much, at the pressures and speeds involved in the flow we are modeling. Within the ...
• 55.7k
Accepted

• 151
1 vote
Accepted

### Finite elements for Stokes with traction boundary conditions

In the meantime we did some more research into this issue and documented our findings in: M. Huber, U. Rüde, C. Waluga, B. Wohlmuth. Highly sparse surface couplings for subdomain-wise isoviscous ...
• 1,074

Only top scored, non community-wiki answers of a minimum length are eligible