[petsc-users] DG within DMPlex

[Jed Brown]

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).
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