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Re: Question about essential boundary conditions

 

Garth N. Wells wrote:


Marie Rognes wrote:
Johan Hoffman wrote:
On Thu, Feb 07, 2008 at 05:43:13PM +0100, Marie Rognes wrote:
Anders Logg wrote:
On Thu, Feb 07, 2008 at 05:07:46PM +0100, Marie Rognes wrote:

Hi,

I would like to construct a vector-valued finite element space where
the
components may be related to each other on the boundary.

Example:

    Let P1 be piecewise linears on K.
    I want the subspace {(u, v) \in P1 x P1 such that u = v on the
boundary of K.}

Is this possible in DOLFIN today?

Not that I know. Generally, we can't handle constraints.


Darn. How hard do you think it would be to set-up?
I don't know. There was some discussion a month back on setting
no-slip constraints (zero normal component on boundaries) which is
similar. I think the conclusion was that we didn't find a general
solution. (But most likely there is one...)

--
Anders
I guess you could set it up as a penalty on (u-v)?


Pardon my ignorance please, but how does this work?


Take a look at

  /src/demo/pde/dg/cpp/Poisson.form

It enforces u = 0 using Nitsche's method. If drop all the *ds terms except

    gamma/h*v*u*ds

you'll get a penalty method.


Ok. Thanks!

--
Marie E. Rognes
Ph.D Fellow, Centre of Mathematics for Applications, University of Oslo
http://folk.uio.no/meg



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