Work

Shape-Preserving C1 and C2 Reconstructions of Discontinuous Functions Using Spline Quasi-Interpolation

Year: 2025

Type: article

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 C1 and C2 reconstructions and preserving essential shape properties. We demonstrate theoretical frameworks showing optimal approximation order O(hd+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.

Source: Mathematics

DOI: 10.3390/math13081237

Authors: Francesc Aràndiga, Sara Remogna

Institutions: Universitat de València, University of Turin

Language: English

Topic: Advanced Numerical Analysis Techniques

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Generalitat Valenciana, Gruppo Nazionale per il Calcolo Scientifico