Consider the domain D := {(x, y)| x ≥ 0, y ≥ 0, 1 ≤ x + y ≤ 2} tiled by 12 triangles Dk, where triangles and nodes are numbered as in Figure 5.13.

a) Set up the index set I with entries Ik = {ik, jk, lk}, which assigns node numbers to the kth triangle for 1 ≤ k ≤ 12.

b) Formulate the assembling algorithm that builds up the global stiffness matrix out of the element stiffness matrices ⎛ ⎜⎝ s (k) 11 s (k) 12 s (k) 13 s (k) 21 s (k) 22 s (k) 23 s (k) 31 s (k) 32 s (k) 33 ⎞ ⎟⎠ for a general index set I and 1 ≤ k ≤ m.

c) The example of Figure 5.13 leads to a banded stiffness matrix. What is the bandwidth?