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

Jed Brown jed at jedbrown.org
Tue Jun 2 11:20:49 CDT 2015

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


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.

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