[petsc-users] DG within DMPlex

[Matthew Knepley]

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.


> local grid adaptation (hp)
>

This is just as easy in cG land.


> convection-diffusion where convection is dominant
>

I have seen the CW Shu papers on this, and I can understand the possible
advantages here.


> fourth order problems (standard C^0 elements can be used)
>

Interior penalty is a possibility for this problem. So are C1 elements,
with which this is rarely compared.
It should also be compared with the NURBS formulations, like IGA.

   Matt


> praveen
>
>
> On Tue, Oct 4, 2016 at 7:58 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Mon, Oct 3, 2016 at 6:36 PM, Justin Chang <jychang48 at gmail.com> wrote:
>>
>>> Hi all,
>>>
>>> Is there, or will there be, support for implementing Discontinuous
>>> Galerkin formulations within the DMPlex framework? I think it would be nice
>>> to have something such as the SIPG formulation for the poisson problem in
>>> SNES ex12.c
>>>
>>
>> We will have a trial DG in PETSc shortly. However, I don't think DG
>> methods make much sense for elliptic
>> problems. Why would I use it there?
>>
>>   Thanks,
>>
>>     Matt
>>
>>
>>> Thanks,
>>> Justin
>>>
>> --
>> 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
>>
>
>


-- 
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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