[CIG-MC] SUPG method in CitcomS

Matthew Knepley knepley at mcs.anl.gov
Sat Apr 7 06:35:00 PDT 2012

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.


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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