Argyris type quasi-interpolation of optimal approximation order

2020 ◽  
Vol 79 ◽  
pp. 101836 ◽  
Author(s):  
Jan Grošelj
Keyword(s):  
Approximation Order ◽  
Optimal Approximation

scholarly journals Bivariate spline interpolation with optimal approximation order

2001 ◽  
Vol 17 (2) ◽  
pp. 181-208 ◽  
Author(s):  
O. Davydov ◽  
G. Nürnberger ◽  
F. Zeilfelder
Keyword(s):  
Spline Interpolation ◽  
Approximation Order ◽  
Optimal Approximation ◽  
Bivariate Spline ◽  
Bivariate Spline Interpolation

scholarly journals Optimal approximation order of piecewise constants on convex partitions

2020 ◽  
Vol 58 ◽  
pp. 101444
Author(s):  
Oleg Davydov ◽  
Oleksandr Kozynenko ◽  
Dmytro Skorokhodov
Keyword(s):  
Approximation Order ◽  
Optimal Approximation ◽  
Convex Partitions

scholarly journals Construction of a normalized basis of a univariate quadratic $C^1$ spline space and application to the quasi-interpolation

2021 ◽  
Vol 40 ◽  
pp. 1-21
Author(s):  
A. Rahouti ◽  
Abdelhafid Serghini ◽  
A. Tijini
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Approximation Order ◽  
Spline Space ◽  
Numerical Results ◽  
Optimal Approximation ◽  
Polar Form ◽  
Piecewise Polynomial ◽  
The Finite Element Method ◽  
Element Method

In this paper, we use the finite element method to construct a new normalized basis of a univariate quadratic $C^1$ spline space. We give a new representation of Hermite interpolant of any piecewise polynomial of class at least $C^1$ in terms of its polar form. We use this representation for constructing several superconvergent and super-superconvergent discrete quasi-interpolants which have an optimal approximation order. This approach is simple and provides an interesting approximation. Numerical results are given to illustrate the theoretical ones.

Interpolatory subdivision schemes with the optimal approximation order

2019 ◽  
Vol 347 ◽  
pp. 1-14 ◽  
Author(s):  
Baoxing Zhang ◽  
Hongchan Zheng ◽  
Weijie Song ◽  
Zengyao Lin ◽  
Jie Zhou
Keyword(s):  
Approximation Order ◽  
Optimal Approximation ◽  
Subdivision Schemes ◽  
Interpolatory Subdivision

scholarly journals SURFACE COMPRESSION WITH HIERARCHICAL POWELL–SABIN B-SPLINES

2006 ◽  
Vol 04 (01) ◽  
pp. 177-196 ◽  
Author(s):  
JAN MAES ◽  
ADHEMAR BULTHEEL
Keyword(s):  
Numerical Experiments ◽  
Approximation Order ◽  
Optimal Approximation ◽  
Compression Rate ◽  
Interpolation Scheme ◽  
Compression Method ◽  
B Splines ◽  
Hierarchical Basis ◽  
High Compression ◽  
Surface Compression

We show how to construct a stable hierarchical basis for piecewise quadratic C1 continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we use a stable quasi-interpolation scheme that achieves optimal approximation order. Numerical experiments demonstrate the high compression rate of the algorithm.

Nonlinear dynamics of pulsating detonation wave with two-stage chemical kinetics in the shock-attached frame

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yaroslava E. Poroshyna ◽  
Aleksander I. Lopato ◽  
Pavel S. Utkin
Keyword(s):  
Wave Propagation ◽  
Detonation Wave ◽  
Model Comparison ◽  
Approximation Order ◽  
Transition Regime ◽  
Stage Model ◽  
Two Stage ◽  
One Dimensional ◽  
Kinetics Of ◽  
Detonation Wave Propagation

Abstract The paper contributes to the clarification of the mechanism of one-dimensional pulsating detonation wave propagation for the transition regime with two-scale pulsations. For this purpose, a novel numerical algorithm has been developed for the numerical investigation of the gaseous pulsating detonation wave using the two-stage model of kinetics of chemical reactions in the shock-attached frame. The influence of grid resolution, approximation order and the type of rear boundary conditions on the solution has been studied for four main regimes of detonation wave propagation for this model. Comparison of dynamics of pulsations with results of other authors has been carried out.

scholarly journals On the Convexity Preservation of a Quasi C3 Nonlinear Interpolatory Reconstruction Operator on σ Quasi-Uniform Grids

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 310 ◽  
Author(s):  
Pedro Ortiz ◽  
Juan Carlos Trillo
Keyword(s):  
Initial Data ◽  
Numerical Experiments ◽  
Approximation Order ◽  
Piecewise Polynomial ◽  
Nonuniform Grids ◽  
Uniform Grids ◽  
Reconstruction Operator ◽  
Convexity Properties ◽  
Second Degree

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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