[Gmsh] The volume of the second order tetrahedron

[Mikhail Artemiev]

>> Hello, Geordie.
>> Thank you for reply.
>> I used "Tools - Visibility - Numeric - Mesh - Hide all elements - Show
>> Element (for instance, 1365)" to draw that figure.
>
> Oh right, O.K.  It's a funny looking shape, isn't it.  Perhaps that's
> just how Gmsh depicts nonlinear elements?

It's a very important question!
Please, look at 2 figures:
this is a shpere that was approximated by first order tets 
http://saveimg.ru/show-image.php?id=47cdfa0e6f7a01f5dee8880c7081e151
this is a sphere that was approximated by second order tets 
http://saveimg.ru/show-image.php?id=fa66051392be4e36e2262055272170e1
These 2 meshes was created by gmsh from one geo file (and with the same 
characteristic lengths).
I will wonder if it is a feature of visualization.
Standard 10-node second order tetrahedron differs from 4-node first order 
tetrahedron by adding 6 node in the middles of the edges of tetrahedron.
I think that gmsh not only adds new 6 nodes but changes the coordinates of 
these nodes too.
Therefore we have nonstandard 10-node quadratic tetrahedron and the formulae 
of the shape functions defined on the standard one don't work.
Am I wrong?

Mikhail Artemiev

>
>> To create the mesh I used command "gmsh mygeo.geo -3 -bin -order 2 -o
>> mymesh.msh", therefore following the manual the elements of the mesh are
>> 10-node second order tetrahedra.
>
> That's all pretty standard.
>
>> I don't know is this gmsh element a standart 10-node quadratic 
>> tetrahedron or not.
>
> I suppose it doesn't matter so much what Gmsh thinks as what your
> finite element solver thinks?  I'd say it's free to interpret Gmsh
> type-11 elements as quadratic tetrahedra.
>
>> I will see the formulae. I hope that they will help me.
>
> O.K.  Let us know if you get stuck, or rather write to the list; I
> think that's better in general, because others might know the answer
> better or sooner than me, and also it saves it for posterity.