[petsc-users] DG within DMPlex

[Matthew Knepley]

On Tue, Oct 4, 2016 at 10:43 AM, Jed Brown <jed at jedbrown.org> wrote:

> Matthew Knepley <knepley at gmail.com> writes:
>
> > On Tue, Oct 4, 2016 at 10:23 AM, Jed Brown <jed at jedbrown.org> wrote:
> >
> >> Matthew Knepley <knepley at gmail.com> writes:
> >>
> >> > On Mon, Oct 3, 2016 at 9:51 PM, Praveen C <cpraveen at gmail.com> wrote:
> >> >
> >> >> DG for elliptic operators still makes lot of  sense if you have
> >> >>
> >> >> problems with discontinuous coefficients
> >> >>
> >> >
> >> > This is thrown around a lot, but without justification. Why is it
> better
> >> > for discontinuous coefficients? The
> >> > solution is smoother than the coefficient (elliptic regularity). Are
> DG
> >> > bases more efficient than high order
> >> > cG for this problem? I have never seen anything convincing.
> >>
> >> CG is non-monotone and the artifacts are often pretty serious for
> >> high-contrast coefficients, especially when you're interested in
> >> gradients (flow in porous media).  But because the coefficients are
> >> under/barely-resolved, you won't see any benefit from high order DG, in
> >> which case you're just using a complicated/expensive method versus
> >> H(div) finite elements (perhaps cast as finite volume or mimetic FD).
> >>
> >
> > I was including H(div) elements in my cG world. Is this terminology
> wrong?
>
> It's not a continuous basis....
>
> Perhaps ambiguous.
>

I think cG should refer to Conforming Galerkin, since that is really what
is implied.
DG and H(div) are both non-conforming. So I really want to cG/nG dichotomy.

   Matt

-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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