Moment preserving local spline projection operators

Martin Campos Pinto (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 CNRS - Centre National de la Recherche Scientifique

This article describes an elementary construction of a dual basis for non-uniform B-splines that is local, L ∞-stable and reproducts polynomials of any prescribed degree. This allows to define local projection operators with near-optimal approximation properties in any L q , 1 ≤ q ≤ ∞, and high order moment preserving properties. As the dual basis functions share the same piecewise polynomial structure as the underlying splines, simple quadrature formulas can be used to compute the projected spline coefficients.

Mots clés: Preservation of moments; Splines; Stable dual bases; Projection operators

Domaines: Analyse numérique [math.NA]

Martin Campos Pinto. Moment preserving local spline projection operators. Constructive Approximation, 2020, 51 (3), pp.565-585. ⟨10.1007/s00365-019-09474-1⟩. ⟨hal-01837912v2⟩