On the convexity preservation of a quasi C3 nonlinear interpolatory reconstruction operator on σ quasi-uniform grids
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Knowledge AreaMatemática Aplicada
SponsorsThis research was funded by the FUNDACIÓN SÉNECA, AGENCIA DE CIENCIA Y TECNOLOGÍA DE LA REGIÓN DE MURCIA grant number 20928/PI/18, and by the Spanish national research project PID2019-108336GB-I00.
Bibliographic CitationOrtiz, P.; Trillo, J.C. On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids. Mathematics 2021, 9, 310. https://doi.org/10.3390/math9040310
Class quasi C3
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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