[aspect-devel] Progress in writing the mantle convection code Aspect

[Wolfgang Bangerth]

> It sounded like Eric made an "evil" example where a larger value is
> acceptable and that is why I mentioned the option to increase the
> parameters. I mean if the only measure is the amount of overshoot, we
> can just do an O(1) first order diffusion and smear everything out.
> :-)

To everone's surprise, Jean-Luc Guermond showed that the first order diffusion 
is not actually monotone (i.e., that over/undershoots can not be avoided even 
if you make beta large) if (and only if) you are in 3d and have quadratic or 
higher elements. I think that's a pretty crazy result!

That said, he's come up with a scheme that replaces the traditional first 
order scheme by something that *is* monotone and, furthermore, that avoids the 
difficulty of defining what the mesh size h needs to be in defining the 
artificial diffusion. There is no second order scheme yet, though.

I don't know whether that's something relevant to the immediate debate -- I 
think we should still see if there's something that can be done about playing 
with the regularization parameters. It's something keeping in mind for the 
future, though. For now, there is nothing to show -- his paper isn't even 
submitted yet :-)

Cheers
  W.


-- 
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Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/