[aspect-devel] Q2P-1 question

[Wolfgang Bangerth]

On 11/02/2016 06:25 AM, Thieulot, C.A.P. (Cedric) wrote:
>
> I was reading on the Q2P-1 element recently when I came across the
> literature about the mapping of the pressure (e.g. Finite element
> approximation on quadrilateral meshes,
> Arnold et al, Commun. Numer. Meth. Engng 2001; 17:805–812 (DOI:
> 10.1002/cnm.450) ). To summarize it I rereby attach a slide from a
> presentation of Arnold.
> I was then wondering which option is implemented in ASPECT ?
>

You mean whether we do or do not map the pressure from the reference 
cell to the real cell?

We use FE_DGP if we want to use a discontinuous pressure, which is 
mapped from the reference cell. Arnold's answer is not wrong, but it 
only matters if you have cells that deviate strongly from cubes because 
in that case the norm of the Jacobian of the mapping is large and the 
norm enters the approximation quality. For the cells we use, I would 
venture the guess that the norm is never much larger than 2 or 3 -- 
almost all of our cells are close to cubes. In that case, I doubt that 
it would make much of a difference.

But if you'd like to try, you can change the new_FE_Q_or_DGQ in 
source/simulator/introspection.cc from using FE_DGP to using 
FE_DGPNonparametric, and in that case we use a non-mapped element. It's 
a one-line change. You could try whether that makes any noticeable 
difference.

Best
  W.

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