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Error analysis for local coarsening in univariate spline spaces

Author

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  • Figueroa, Silvano
  • Garau, Eduardo M.
  • Morin, Pedro

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.

Suggested Citation

  • Figueroa, Silvano & Garau, Eduardo M. & Morin, Pedro, 2024. "Error analysis for local coarsening in univariate spline spaces," Applied Mathematics and Computation, Elsevier, vol. 472(C).
    • Handle: RePEc:eee:apmaco:v:472:y:2024:i:c:s0096300324000882
    DOI: 10.1016/j.amc.2024.128616
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