[petsc-users] DG within DMPlex

[Matthew Knepley]

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?

  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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