  We discuss a discretization by polygonal lines of the Euler-Bernoulli bending
energy and of Euler elasticae under clamped boundary conditions. We show
Hausdorff convergence of the set of almost minimizers of the discrete bending
energy to the set of smooth Euler elasticae under mesh refinement in (i) the
$W^{1,\infty}$-topology for piecewise-linear interpolation and in (ii) the
$W^{2,p}$-topology, $p \in{[2,\infty[}$, using a suitable smoothing operator to
create $W^{2,p}$-curves from polygons.
