Seyed,

Generally, in FEM you number elements like in the below picture:

<https://lh3.googleusercontent.com/-0n-HlF1EsRs/WLBEmN34aaI/AAAAAAAAAGU/GlK9R9OqDJ8FSTLKGXeaI85eU6pdV3MkwCLcB/s1600/System.png>

No, that is patently wrong. First, you are only considering rectangular domains subdivided into rectangular cells. Second, you think that because there is a "simple" numbering that that is what codes "should do". Both of these assumptions are wrong. How, for example, should a code number these cells:

https://raw.githubusercontent.com/dealii/dealii/master/doc/doxygen/images/distributed_mesh_1.png

https://raw.githubusercontent.com/dealii/dealii/master/doc/doxygen/images/hyper_shell_96_cut.png

Starting a sentence with "Generally, in FEM you number elements..." is generally wrong.


I am a bit confused since it is a rather easy task which should not be
such a big "deal" in deal.II.

Because it's *not* easy. It's only easy if you consider simple situation like yours. But if you want to do complicated things, they generally turn out to be complicated.

Best
 W.

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

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