Add possibility to read in higher order Gmsh file

[jpthiele]

If a gmsh file has quadratic triangle elements defined then they are not recognized as triangles. Maybe we can easily fix this @j-fu ?

[j-fu]

Do you mean isoparametric elements with quadratic edges ? In that case I can imagine two modes:
a) forget the second order info
b) subdivide a triangle into four, using a linear approximation of the edges.

One would have to look into the gmsh data structure. I don't expect it is complicated, but perhaps a bit of work nevertheless. Is there a concrete example ?

[jpthiele]

I think the first approach would be the right default one and would be the one we need for https://github.com/BAMresearch/NFDI4IngModelValidationPlatform as the problem should then be solved with quadratic finite elements.
Maybe this could issue a warning/info that this is a higher order mesh and higher order methods should be used for solving it as well as that seems to have been the intention?
And reading in a subdivision might be a good alternative option to enable/choose.

As for the underlying structure in Gmsh it's a Triangle6 Element, i.e. elementType=9 and the first three nodes are the outer ones,
i.e.

Triangle:        Triangle6:      
v
^
|
2                       2          
|`\                   |`\       
|   `\                5   `4   
|     `\              |      `\  
0------1--> u     0---3---1    

Here is a msh file for a plate with a hole with quadratic elements.

$MeshFormat
4.1 0 8
$EndMeshFormat
$PhysicalNames
5
1 1 "boundary_left"
1 2 "boundary_bottom"
1 3 "boundary_right"
1 4 "boundary_top"
2 1 "surface"
$EndPhysicalNames
$Entities
6 5 1 0
1 0 0 0 0 
2 0.33 0 0 0 
3 1 0 0 0 
4 1 1 0 0 
5 0 1 0 0 
6 0 0.33 0 0 
1 0.33 0 0 1 0 0 1 2 2 2 -3 
2 1 0 0 1 1 0 1 3 2 3 -4 
3 0 1 0 1 1 0 1 4 2 4 -5 
4 0 0.3300000000000001 0 0 1 0 1 1 2 5 -6 
5 0 2.775557561562891e-17 0 0.33 0.33 0 0 2 6 -2 
1 0 0 0 1 1 0 1 1 5 1 2 3 4 5 
$EndEntities
$Nodes
11 51 1 51
0 2 0 1
1
0.33 0 0
0 3 0 1
2
1 0 0
0 4 0 1
3
1 1 0
0 5 0 1
4
0 1 0
0 6 0 1
5
0 0.33 0
1 1 0 3
6
7
8
0.6649999999989589 0 0
0.4974999999994727 0 0
0.8324999999995628 0 0
1 2 0 3
9
10
11
1 0.4999999999986942 0
1 0.2499999999994195 0
1 0.7499999999993471 0
1 3 0 3
12
13
14
0.500000000002059 1 0
0.7500000000008381 1 0
0.2500000000010296 1 0
1 4 0 3
15
16
17
0 0.6650000000010193 0
0 0.8325000000004071 0
0 0.4975000000006284 0
1 5 0 3
18
19
20
0.2333452383332417 0.2333452372498797 0
0.1262855330554268 0.3048802455734165 0
0.3048802458660948 0.1262855323488387 0
2 1 0 31
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
0.1959439281524296 0.479674165201504 0
0.4607730582016283 0.3906619234225345 0
0.2908264624533337 0.7254034792111053 0
0.649243226095195 0.6624668562888789 0
0.7120860473825436 0.2857129206375196 0
0.4802408687832745 0.1819440162619868 0
0.1454132312266669 0.8627017396055526 0
0.3954132312276963 0.8627017396055526 0
0.8560430236912717 0.3928564603181069 0
0.8560430236912717 0.1428564603187598 0
0.328358493177029 0.4351680443120193 0
0.375799760327481 0.5580327013168199 0
0.2433851953028817 0.6025388222063046 0
0.8246216130475975 0.8312334281444395 0
0.8246216130475975 0.5812334281437865 0
0.09797196407621482 0.404837082600752 0
0.09797196407621482 0.5723370826012617 0
0.6885430236907513 0.1428564603187598 0
0.5726204343911168 0.09097200813099339 0
0.4051204343916373 0.09097200813099339 0
0.574621613048627 0.8312334281444395 0
0.1454132312266669 0.6952017396060624 0
0.5550081421484117 0.5265643898557067 0
0.4700348442742643 0.6939351677499921 0
0.3567930535582581 0.2076446267559332 0
0.2146445832428357 0.3565097012256918 0
0.586429552792086 0.3381874220300271 0
0.6806646367388693 0.4740898884631993 0
0.347059148267435 0.3120035803362071 0
0.4705069634924515 0.2863029698422607 0
0.596163458082909 0.2338284684497532 0
$EndNodes
$Elements
5 28 1 28
1 1 8 2
1 1 6 7 
2 6 2 8 
1 2 8 2
3 2 9 10 
4 9 3 11 
1 3 8 2
5 3 12 13 
6 12 4 14 
1 4 8 2
7 4 15 16 
8 15 5 17 
2 1 9 20
9 12 4 23 14 27 28 
10 2 9 25 10 29 30 
11 21 22 23 31 32 33 
12 9 3 24 11 34 35 
13 15 5 21 17 36 37 
14 6 2 25 8 30 38 
15 1 6 26 7 39 40 
16 3 12 24 13 41 34 
17 4 15 23 16 42 27 
18 23 22 24 32 43 44 
19 18 1 26 20 40 45 
20 5 18 21 19 46 36 
21 24 22 25 43 47 48 
22 9 24 25 35 48 29 
23 21 18 22 46 49 31 
24 22 18 26 49 45 50 
25 15 21 23 37 33 42 
26 6 25 26 38 51 39 
27 25 22 26 47 50 51 
28 12 23 24 28 44 41 
$EndElements