On Sun, 22 Apr 2007, li pan wrote:
> I have mathematic problem which I thought long time.
> I'm not a mathematician and the people around me can
> not help me either. I hope any mathematic experts can
> give some advice.
> The question is: how to discretise
> grad(div(u)) with Galerkin method?
Well, I think by the definition of Galerkin the discretization will
be:
(grad(div(u)), v)
Which you'll normally integrate by parts out to:
(div(u), div(v)) plus boundary terms.
Unless this is a relatively unimportant term in a larger problem,
though, trying to solve equations based on this will give you some
trouble. Notice that you can add any divergencefree vector field to
u, or any compactlysupported divergencefree field to v, without
changing the value of the bilinear form. So if you're just trying to
solve something like "grad(div(u)) = f", you'll have a singular system
(and depending on curl(f), possibly an insoluble system) on your hands.

Roy
