Error analysis for local coarsening in univariate spline spaces

Silvano Figueroa, Eduardo M. Garau and Pedro Morin

Applied Mathematics and Computation, 2024, vol. 472, issue C

Abstract: In this article we analyze the error produced by the removal of an arbitrary knot from a spline function; we consider the L2-, the H1- and the L∞-errors. 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 coefficients 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.

Keywords: Data reduction; Knot removal; Coarsening; Compression; B-splines (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324000882

DOI: 10.1016/j.amc.2024.128616

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