? on mixed formulation for incompressible flow
 

Hi,

I am developing a parallel code for transient incompressible N-S using finite element method. for some reasons I like to use mixed formulation and element-by-element architecture. To make sure the iteration converges and converges in a nice way, I have to find a good preconditioner for the linear solver, which must be invertible and can be inverted quickly and should use as less as possible memory storage. A matrix created by the diagonal terms of the global stiffness matrix (which in fact is never assembled in EBE) with all other terms set to zero is my favorite.

However, due to absence of pressure in continuity equation, the matrix I got inherently has zeros on the diagonal.

I heard there are ways to get around this difficulty, but what are they?

Re: ? on mixed formulation for incompressible flow
 

1) Look for penalty methods, projection schemes, artificial compressibility. 2) When dealing with incompressible flows with FEM methods (or other discretization schemes): is it almost mandatory to use different space of approximation for velocity and pressure to avoid false pressure modes.