Element-wise DOF numbering and shape function numbering

[Lixing Zhu]

Hi all,

I am playing with a vector-valued 2D problem (displacement vector u and v). Since I need to use the shape functions of a specific vertex, I export the DOFs numbering and its corresponding number of the vertex. As illustrated in FiniteElement, for quadratic 2D FE_Q element, the pair of DODs of a specific vertex are grouped as follows:

#DOF, #component, #within the base

0 0 0

1 1 0

2 0 1

3 1 1

4 0 2

5 1 2

6 0 3

7 1 3

8 0 4

9 1 4

10 0 5

11 1 5

12 0 6

13 1 6

14 0 7

15 1 7

16 0 8

17 1 8

However, for high-order elements (higher than or equal to 3), this pattern no longer exists. In other words, the DOFs of the same vertex are not grouped. Take 4th order 2D FE_Q as an example,

#DOF, #component, #within the base

0 0 0

1 1 0

2 0 1

3 1 1

4 0 2

5 1 2

6 0 3

7 1 3

8 0 4

9 0 5

10 0 6

11 1 4

12 1 5

13 1 6

14 0 7

15 0 8

16 0 9

17 1 7

18 1 8

19 1 9

20 0 10

21 0 11

22 0 12

23 1 10

24 1 11

25 1 12

26 0 13

27 0 14

28 0 15

29 1 13

30 1 14

31 1 15

32 0 16

33 0 17

34 0 18

35 0 19

36 0 20

37 0 21

38 0 22

39 0 23

40 0 24

41 1 16

42 1 17

43 1 18

44 1 19

45 1 20

46 1 21

47 1 22

48 1 23

49 1 24

I guess this suggests that we cannot simply assume the pairing of DOFs in vector-valued problems. My question is, is the numbering of the DOF is fixed among the same type of elements? Since I need to fetch the DOFs of a specific vertex, I guess FiniteElement::component_to_system_index() can help determine the current DOF number of a specific vertex. Do I need to check them for each element? or just check it once for a certain type of element?

Regards,

Lixing

[Daniel Arndt]

Lixing,

Yes, using FiniteElemnt::component_to_system_index() seems to be reasonable to use to identify the overall DoF number for copies of the same finite element. The FiniteElement class doesn't need class accessor argument and the mapping is thus generic.

Also note that there is DoFTools::map_dofs_to_support_points and DoFTools::map_support_points_to_dofs that might be helpful for you.

Best,

Daniel

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[Lixing Zhu]

Hi Daniel,

Thanks. I'll also look into  DoFTools::map_dofs_to_support_points and  DoFTools::map_support_points_to_dofs.

Regards,

Lixing