[dune-pdelab] Instationary Navier-Stokes equations with Finite Volume method

[Christian Engwer]

Hi,

> I use classes from stokesdg.hh  as local operators and P0LocalFiniteElementMap as finite element map for pressure and velocity components. My idea was to turn discontinuous Galerkin case into finite volume method  by using a zero order polynomial (P0LocalFiniteElementMap).
> 
> This method doesn’t seem to work, do you think the classes I use are appropriate to solve these equations ? I am aware of the existence of StokesDGVectorFEM but I’m not quite sure about how it works.

the problem is not DUNE related, but due to the maths. The p0/p0 pair
does not fulfill the inf-sup condition and thus you get wrong
results. Furthermore the DG method is not a FV method, although they
have a lot of similarities. In particular, you have to be careful
regarding the definition of your fluxes.

> Are there any other local operators I can try ?

you should write your own operator. And! more important first think
about which discretization you want to use.

You'll have to either use a pair like P1/P0, or use a stabilization,
like LPS, or other techniques.

Ciao
Christian