1. Triangulation No of elements = 16 No of nodes = 13 No interior nodes = 5 No of boundary nodes = 8

2. With the triangulation we associate the function space consisting of continuous, piecewise linear functions on vanishing on i.e Triangulation No interior nodes = 5 No of global basis functions = 5

3. 1 2 3 4 5 6 7 8 9 10 11 12 13 Element Labeling 14 15 16

4. Node Labeling (global labeling) 12 34 5 6 7 8 9 1011 1213

5. global basis functions 12 34 5 6 7 8 9 1011 1213

6. 12 34 5 6 7 8 9 1011 1213 global basis functions

7. Global basis functions

8. global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312

9. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

10. global basis functions 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0

11. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 12 34 5 6 7 8 9 1011 1213 Assemble linear system

12. 12 34 6 7 8 9 0 0 0 0 0 0 0 0 0 0 0 0 1011 5 1312 12 34 6 7 8 9 0 0 0 0 0 0 0 0 1011 5 1312 0 0

13. Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913

14. Node Label (local labeling) 12 3 Each triangle has 3 nodes. Label them locally inside the triangle

15. Node and Element Label

16. Local label.vs. global label Matrix t(3,#elements) 16151413121110987654321 131211105555432132141 1211101312111013 12111087692 8769131211108769121110133

17. X-coordinate and y-coordinate Matrix p(2,#elements) 13121110987654321 0.750.25 0.7510.50 1001x 0.25 0.75 0.50 1 0011y

18. Boundary node vector e(#boundary node) e8e7e6e5e4e3e2e1 98764321start 14329876end

19. Approximation of u 01 02 03 04 0.0695 06 07 08 09 0.04910 0.04911 0.04912 0.04913

20. Global basis functions

21. Triangulation