[petsc-users] DG within DMPlex

[Jed Brown]

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.
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