fenics team mailing list archive

[Gideon Simpson <grs2103@xxxxxxxxxxxx>]

Ok, I see the error.  However, would you expect Poisson + zero  
Dirichlet data to no longer have a symmetric matrix?
-gideon

On Jan 8, 2008, at 3:17 AM, Garth N. Wells wrote:

> Gideon Simpson wrote:
> > Something I discovered that I'm hoping someone will clarify is the  
> > following.  Let A be the matrix associated with a Finite Element  
> > formulation of Poisson's equation, as in the example in the demo  
> > directory.  If one exams the eigenvalues of A before the  
> > application of the BC's, there is a zero eigenvalue, while  
> > afterwards, there is no such troublemaker.
>
> This is correct. What it's telling you is that you need to supply a  
> Dirichlet boundary condition to ensure that the solution is unique.
>
> > Thinking of A in terms of its associated weak form, I fully  
> > expected A to be a positive definite, symmetric matrix.  This is  
> > not the case.
> Inspecting of the form, I would expect a positive semi-definite  
> matrix if you don't say anything about the value of functions at  
> the boundary.
>
> Garth
>
> > -gideon
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