  In this article we analyze the error produced by the removal of an arbitrary
knot from a spline function. When a knot has multiplicity greater than one,
this implies a reduction of its multiplicity by one unit. In particular, we
deduce a very simple formula to compute the error in terms of some neighboring
knots and a few control points of the considered spline. Furthermore, we show
precisely how this error is related to the jump of a derivative of the spline
at the knot. We then use the developed theory to propose efficient and very
low-cost local error indicators and adaptive coarsening algorithms. Finally, we
present some numerical experiments to illustrate their performance and show
some applications.
