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...
| Autores: | , |
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| 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 |
| 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. |
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