%0 Journal Article 
%A Ortiz Herranz, Pedro
%A Trillo Moya, Juan Carlos
%T On the convexity preservation of a quasi C3 nonlinear interpolatory reconstruction operator on σ quasi-uniform grids
%D 2021
%@ 2227-7390
%U http://hdl.handle.net/10317/10575
%X This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as its reproduction of second-degree polynomials, approximation order, and conditions for convexity preservation. In particular, for σ quasi-uniform grids with σ≤4, we get a quasi C3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.
%K Matemática Aplicada
%K Interpolation
%K Reconstruction
%K Nonlinearity
%K Nonuniform
%K σ quasi-uniform
%K Convexity
%K Class quasi C3
%K 12 Matemáticas
%K 1206.07 Interpolación, Aproximación y Ajuste de Curvas
%~ GOEDOC, SUB GOETTINGEN