[CIG-MC] SUPG method in CitcomS

[Matthew Knepley]

On Sat, Apr 7, 2012 at 1:41 AM, Jed Brown <five9a2 at gmail.com> wrote:

> On Fri, Apr 6, 2012 at 22:20, Matthew Knepley <knepley at mcs.anl.gov> wrote:
>
>> Can't you also do WENO reconstruction on an FEM solution?
>>
>
> It's much less natural and rarely done in practice.
>
>
>> Okay, that was not how it was explained to me. Is it like a Laplacian
>> filer (which would sharpen edges)? I don't see how this would reduce
>> oscillation,
>> although I guess it could result from the solve for the conservation
>> requirement.
>>
>
> Look at the algorithm, it is a discrete interface sharpening filter.
>
> http://www.agu.org/pubs/crossref/1993/92JB02858.shtml
>
> It clips values that are greater than 1 or less than 0, tracking the
> maximum over/undershoot. Values inside the bounds of that over/undershoot
> are then pressed out to 1 and 0 respectively. Then the remaining
> conservation error is distributed to all cells that are not identically 0
> or 1. I don't see any way that this is sensible for thermodynamics.
>

It will get rid of oscillation and conserve the quantity (looks a little
like FCT), but the 0,1 bounds make no sense to me
for energy. For concentration (as in the paper), they are natural.

    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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