dolfin team mailing list archive

[Shawn Walker <walker@xxxxxxxxxxxxxxx>]

On Mon, 15 Sep 2008, Anders Logg wrote:

> On Mon, Sep 15, 2008 at 11:21:59AM +0100, Garth N. Wells wrote:
> > DOLFIN wrote:
> > > One or more new changesets pushed to the primary dolfin repository.
> > > A short summary of the last three changesets is included below.
> > >
> > > changeset:   4754:23602808c60413cb8faffca818e7a8c04527d3ec
> > > tag:         tip
> > > user:        Anders Logg <logg@xxxxxxxxx>
> > > date:        Sun Sep 14 19:46:40 2008 +0200
> > > files:       demo/pde/elasticity/python/demo.py
> > > description:
> > > Use symmetric gradient in variational form in elasticity demo
> >
> > In particular reason for this? It is simpler (and still correct) to use
> > the gradient.
> >
> > Garth
>
> To make the form and the matrix symmetric. I showed the demo to a
> friend (in computational mechanics) and he insisted that we replace
> grad(v) by epsilon(v).
>
> --
> Anders

It should be epsilon(v).  In the case of Stokes (or Navier-Stokes), if the 
velocity boundary conditions are dirichlet, then you can just use grad(v). 
However, if you have stress boundary conditions this is no longer true. 
The Dirichlet case lets you simplify the variational form from the 
epsilon(v) case by some integration by parts.  epsilon(v) is the correct 
way.

Incidentally, this means that any "general" Navier-Stokes demos should 
probably be done with the epsilon(v) for the viscous term.  It won't make 
a difference if the boundary conditions are dirichlet for velocity.

- Shawn