fenics team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

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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