How to apply divergence free (∇.v=0) in nodal finite element method?

[mdn]

I know how to apply boundary condition like Dirichlet, Neumann and Robin but i have been struggling to apply divergence free condition for Maxwells or Stokes equations in nodal finite element method. to overcome this difficulties a special element was developed called as edge element but i don't want to use this element because my complete programming depends on the nodal base element.

 

[pasmith]

Divergence free is not usually a boundary condition; it is, certainly in both the examples you give, a condition which is true throughout the domain. The way to enforce it is to express your vector field in a manner which satisfies the condition automatically.

For 2D problems, use a stream function.

For 3D problems, you can use a toroidal-poloidal decomposition.

 

[mdn]

Can I use such potential formulation for curl, curl equation of Maxwell or Navier- Stokes equation in fluid flow?

 

[mdn]

Would you give me the example of NS equation using stream function in fem?