On a class of three points cell-average multiresolution schemes

Sergio Amat (1) , Jacques Liandrat (2) , Maria Moncayo (1) , Juan Ruiz (3) , Juan Carlos Trillo (1)

1 Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena
2 I2M - Institut de Mathématiques de Marseille
3 Departamento de Matematicas [Alcala de Henares]

This paper is devoted to the construction and analysis of a new family of three-points nonlinear cell-average subdivision (multiresolution) schemes. They are based on a centered piecewise nonlinear reconstruction adapted to discontinuities. Some theoretical properties of these schemes (convergence, order of approximation, preservation of the monotonicity in the data, stability or absence of the Gibbs phenomenon) are analyzed. Finally, various numerical examples are presented. (C) 2017 International Association for Mathematics and Computers in Simulation (IMACS).

Mots clés: Cell-average framework; Adaptive reconstructions; Nonlinear means; Subdivision schemes; Multiresolution schemes

Domaines: Analyse numérique [math.NA]

Sergio Amat, Jacques Liandrat, Maria Moncayo, Juan Ruiz, Juan Carlos Trillo. On a class of three points cell-average multiresolution schemes. Mathematics and Computers in Simulation, 2018, 148, pp.66-93. ⟨10.1016/j.matcom.2017.11.007⟩. ⟨hal-02057440⟩