On the Convexity Preservation of a Quasi C 3 Nonlinear Interpolatory Reconstruction Operator on ? Quasi-Uniform Grids

Pedro Ortiz and Juan Carlos Trillo
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Pedro Ortiz: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain
Juan Carlos Trillo: Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 30202 Cartagena, Spain

Mathematics, 2021, vol. 9, issue 4, 1-18

Abstract: 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 ? quasi-uniform grids with ? ? 4 , we get a quasi C 3 reconstruction that maintains the convexity properties of the initial data. We give some numerical experiments regarding the approximation order and the convexity preservation.

Keywords: interpolation; reconstruction; nonlinearity; nonuniform; ? quasi-uniform; convexity; class quasi C 3 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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