Single free node on a four-triangle mixed-boundary mesh ($2U_B=1/2,U_B=1/4$)

Triangulate the region $0\le x,y\le 2$, $x+y\ge 2$ by $x=1$, $y=1$, and $x+y=3$. Impose zero Dirichlet data on the horizontal and vertical exterior edges and zero Neumann data on the sloping edge. Only the midpoint $B=(1,1)$ of the sloping edge remains free in the continuous piecewise linear space. For source one, its stiffness entry is $1/2+1/2+1=2$, while its load is three triangle contributions of $1/6$. The single free value is therefore $1/4$.