  We discuss a semi-implicit numerical scheme that allows for minimizing the
bending energy of curves within certain isotopy classes. To this end we
consider a weighted sum of the bending energy and the tangent-point functional.
Based on estimates for the second derivative of the latter and a uniform
bi-Lipschitz radius, we prove a stability result implying energy decay during
the evolution as well as maintenance of arclength parametrization. Finally we
present some numerical experiments exploring the energy landscape, targeted to
the question how to obtain global minimizers of the bending energy in knot
classes, so-called elastic knots.
