 Solution

ID: past-exam-of-the-approximation-theory-and-finite-element-methods-course-of-the-university-of-oxford/2007/b/6/i/solution

Besides

A, B, C

D = (1, 2)

E = (2, 1)

and

F = (2, 2)

. The four triangles are

A B D

BCE

B D E

and

D EF

, each of area

1/2

. The nodal function is one at

B

, zero at every other node, and affine on each triangle. The vertex conditions give

ϕ_{B} (x, y) = ⎩ ⎨ ⎧ 2 - y, 2 - x, 3 - x - y, 0, (x, y) \in A B D, (x, y) \in BCE, (x, y) \in B D E, (x, y) \in D EF .

The formulas agree on every shared edge, proving continuity.

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