On the convexity preservation of a quasi C3 nonlinear interpolatory reconstruction operator on σ quasi-uniform grids

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 p...

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Detalles Bibliográficos
Autores: Ortiz Herranz, Pedro, Trillo Moya, Juan Carlos
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:España
Institución:Universidad Politécnica de Cartagena(UPCT)
Repositorio:Repositorio Digital UPCT
OAI Identifier:oai:repositorio.upct.es:10317/10575
Acceso en línea:http://hdl.handle.net/10317/10575
https://www.mdpi.com/2227-7390/9/4/310
Access Level:acceso abierto
Palabra clave:Interpolation
Reconstruction
Nonlinearity
Nonuniform
σ quasi-uniform
Convexity
Class quasi C3
Matemática Aplicada
12 Matemáticas
1206.07 Interpolación, Aproximación y Ajuste de Curvas
Descripción
Sumario: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.