Past exam of the approximation theory and finite element methods course of the University of Oxford / 2007 / B / 6 / i

Besides $A,B,C$, set $D=(1,2)$, $E=(2,1)$ and $F=(2,2)$. The four triangles are $ABD$, $BCE$, $BDE$ and $DEF$, 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 giveThe formulas agree on every shared edge, proving continuity.