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

[Wolfgang Bangerth]

On 10/18/2013 08:58 AM, Timo Heister wrote:
>> 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!
>
> Does that mean switching to linear elements for
> temperature/composition might be a good idea?

It just means that a first order artificial diffusion can achieve no 
over/undershoots with linear elements. But they're almost certainly going to 
be much less accurate. I don't think they're generically a better choice.

Best
  W.

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