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Shape-Preserving C 1 and C 2 Reconstructions of Discontinuous Functions Using Spline Quasi-Interpolation

Author

Listed:
  • Francesc Aràndiga

    (Departament de Matemàtiques, Universitat de València, Av. Vicent Andrés Estellés, E-46100 Burjassot, Spain)

  • Sara Remogna

    (Department of Mathematics “G. Peano”, University of Torino, Via Carlo Alberto 10, 10123 Torino, Italy)

Abstract

This paper addresses fundamental challenges in numerical approximation methods, focusing on balancing accuracy with shape-preserving properties. We present novel approaches that combine traditional spline methods with modern numerical techniques, extending existing quasi-interpolation techniques based on B-splines. Our methods maintain computational efficiency while better handling discontinuities, achieving C 1 and C 2 reconstructions and preserving essential shape properties. We demonstrate theoretical frameworks showing optimal approximation order O ( h d + 1 ) , d = 2 , 3 , with local reconstruction. Numerical experiments confirm significant improvements in accuracy and smoothness near discontinuities compared to existing methods, particularly in image processing and shock-capturing applications.

Suggested Citation

  • Francesc Aràndiga & Sara Remogna, 2025. "Shape-Preserving C 1 and C 2 Reconstructions of Discontinuous Functions Using Spline Quasi-Interpolation," Mathematics, MDPI, vol. 13(8), pages 1-20, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:8:p:1237-:d:1631239
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