Re: [Libmesh-users] mathematic help

[Roy S. <roy...@ic...>]

On Sun, 22 Apr 2007, li pan wrote:

> hi Roy,
> thank you for your answer. How did you come up to
> (divu,divv)? Integration by parts says:
> (grad(u),v)=surface_termn - (u,grad(v)). I don't know
> how to deduce it?

Start with this term:

div((div(u))*v) =

Using index notation, with summation over repeated indices

D_i((D_j u_j) v_i) =

Use the product rule for derivatives:

D_i((D_j u_j) v_i) = (D_i (D_j u_j)) v_i + (D_j u_j) (D_i v_i)

i.e.

div((div(u))*v) = grad(div(u))*v + div(u)*div(v)
grad(div(u))*v = div((div(u))*v) - div(u)*div(v)

Then integrate both sides - the left hand side is the Galerkin term
you started with; the right is the boundary term and the symmetric
term you end with.
---
Roy