2023/09/06 by Silvano Figueroa, Figueroa, Silvano, Eduardo M. Garau +3 · 1 citation
Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Tribology and Lubrication Engineering
paper · pdf · doi:10.48550/arxiv.2309.03176
openalex publication_date 2023/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.