On a class of three points cell-average multiresolution schemes

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,...

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Bibliographic Details
Published in:Mathematics and computers in simulation 2018-06, Vol.148, p.66-93
Main Authors: Amat, S., Liandrat, J., Moncayo, M., Ruiz, J., Trillo, J.C.
Format: Article
Language:English
Subjects:
Adaptive reconstructions
Cell-average framework
Mathematics
Multiresolution schemes
Nonlinear means
Numerical Analysis
Subdivision schemes
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Summary: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.
ISSN:0378-4754
1872-7166
DOI:10.1016/j.matcom.2017.11.007