dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Sep 15, 2008 at 09:44:38AM -0400, Shawn Walker wrote:
>
> 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).
>>
>
> 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

To me it looks like it's the opposite: multiply -div sigma(u) = f with
a test function, then integrate by parts getting grad(v), then
noticing that grad(v) may be replaced by epsilon(v) since sigma(v) is
symmetric.

-- 
Anders

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