Enforcing convergence of derivatives for L∞ approximation of a regular curve

Converging approximation of a regular curve by polygonal lines in the uniform norm does not imply convergence discrete differentials to their smooth counterpart. In this paper, we provide constructive approach that, given converging polygon sequence and an its distance objective curve, provides another polygons for which occurs as well. This is based on notion local scale uses multi-resolution decomposition well non linear smoothing process. We proof some numerical evidence it, with application evaluation solid friction pipe.