[petsc-users] Modified Taylor-Hood elements with piece-wise constant pressure for Stokes equation

[Lawrence Mitchell]

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On 02/06/15 17:20, Jed Brown wrote:
> Lawrence Mitchell <lawrence.mitchell at imperial.ac.uk> writes:
>>> So the mass matrix for CG1+DG0 is singular?
>> 
>> I believe so, yes.
> 
> Fabulous.  Now let's take a one element domain.  What is the norm
> of the vector
> 
> u=((1,1,1),(-1))
> 
> in the "basis" {CG1, DG0}?  Note that this represents the
> continuous function u(x,y)=0.
> 
> I assume FEniCS is not using QR to solve the under-determined
> system, so are they silently pinning (e.g., remove the DG0 part
> from one element in the domain)?  If they are just "solving" the
> under-determined systems by hoping that the solver doesn't notice
> that the system is singular, rather than rigorously finding a
> minimum norm solution (expensive), then the discrete solution can
> vary an arbitrary amount by the choice of algebraic solver.

Maybe Justin can chime in here, I don't know, I just happened to know
how the fenics implementation produces the "basis", so proffered that.

> Why does it appear that none of the papers talk about these
> issues?

Pass.

Lawrence
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