Example 5.1 from Eliott's paper:

$\Delta u = f$ on [-2,2]x[-2,2] \ Unit circle
$u = g_D$ on the sides of the square
${\partial u \over \partial n} = g_N$ on unit circle boundary
with
$f = -r^2 \\
u = (r^2+r^{-2})cos(2 \theta) + {r^4 \over 12}(sin^4(\theta)+cos^4(\theta)) \\
g_N = -(x^4+y^4)/3$


I get O(h^2) convergence in L2 norm:

 

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