[petsc-users] Solving/creating SPD systems

[Jed Brown]

Justin Chang <jychang48 at gmail.com> writes:

> Pardon me for my apparent lack of understanding over what may be simple
> concepts, but why is div[u]*div[v] singular in the context of LSFEM?

The corresponding strong form is grad(div(u)).  If u has n*d entries (in
d dimensions -- it is a vector), div(u) has only n entries.  That means
grad(div(u)) must have a null space of dimension at least n*(d-1).

If you a matrix A and a singular matrix B, then

  A + c*B

cannot be well-conditioned for sufficiently large c.
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