[Dune] question about integration element

[Martin Nolte]

Hi Aleksejs,

as long es det is defined as the absolute of the determinant (which I guess 
the Wikipedia-Article does) and J is a square matrix, there is no difference, 
because

- det( A * B ) = det( A ) * det( B )
- det( A^T ) = det( A ).

Notice that the formula you gave at the bottom is obviously wrong if det is 
negative (because there is no negative volume).

Best,

Martin

On 07/29/2014 12:29 PM, Aleksejs Fomins wrote:
> Dear Dune,
>
> The definition of integrationElement is
>
> I = sqrt(| det( J^T J) |)
>
> And the volume is given by
>
> dV' = I dV
>
> Wikipedia tells me that the volume should be
>
> dV' = det(J) dV
>
> What am I missing?
>
> Thank you,
> Aleksejs
>
>
>
> _______________________________________________
> Dune mailing list
> Dune at dune-project.org
> http://lists.dune-project.org/mailman/listinfo/dune
>

-- 
Dr. Martin Nolte <nolte at mathematik.uni-freiburg.de>

Universität Freiburg                                   phone: +49-761-203-5630
Abteilung für angewandte Mathematik                    fax:   +49-761-203-5632
Hermann-Herder-Straße 10
79104 Freiburg, Germany