Splines of Variable Approximation Order and Their Wavelet Decompositions

2019 ◽  
Vol 244 (3) ◽  
pp. 401-418
Author(s):  
Yu. K. Dem’yanovich
Keyword(s):  
Approximation Order ◽  
Wavelet Decompositions

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.

scholarly journals Wavelet Frames for Distributions in Anisotropic Besov Spaces

2005 ◽  
Vol 12 (4) ◽  
pp. 637-658
Author(s):  
Dorothee D. Haroske ◽  
Erika Tamási
Keyword(s):  
Large Class ◽  
Besov Spaces ◽  
Studia Math ◽  
Wavelet Frames ◽  
Anisotropic Besov Spaces ◽  
Wavelet Decompositions

Abstract This paper deals with wavelet frames in anisotropic Besov spaces , 𝑠 ∈ ℝ, 0 < 𝑝, 𝑞 ≤ ∞, and 𝑎 = (𝑎1, . . . , 𝑎𝑛) is an anisotropy, with 𝑎𝑖 > 0, 𝑖 = 1, . . . , 𝑛, 𝑎1 + . . . + 𝑎𝑛 = 𝑛. We present sub-atomic and wavelet decompositions for a large class of distributions. To some extent our results can be regarded as anisotropic counterparts of those recently obtained in [Triebel, Studia Math. 154: 59–88, 2003].

Order-enrichment for categories of partial maps

1995 ◽  
Vol 5 (4) ◽  
pp. 533-562 ◽  
Author(s):  
Marcelo P. Fiore
Keyword(s):  
Approximation Order ◽  
Primitive Notion

Motivated by a desire to treat non-termination directly in the semantics of computation, the notion of approximation between programs is studied in the context of categories of partial maps. In particular, contextual approximation and specialisation are considered and shown to coincide. Moreover, after exhibiting the approximation between total maps as a primitive notion, from an arbitrary (or axiomatic) approximation order on total maps a computationally natural approximation order on partial maps is derived. The main technical contribution is a characterisation of when this approximation order between partial maps is domain-theoretic (in the sense that the category of partial maps Cpo-enriches) provided that the approximation order between total maps is also.

Nested spline–wavelet decompositions

2012 ◽  
Vol 184 (3) ◽  
pp. 282-294
Author(s):  
Yu. K. Dem’yanovich ◽  
I. D. Miroshnichenko
Keyword(s):  
Spline Wavelet ◽  
Wavelet Decompositions

Stabilized hp-DGFEM for Incompressible Flow

2003 ◽  
Vol 13 (10) ◽  
pp. 1413-1436 ◽  
Author(s):  
D. Schötzau ◽  
C. Schwab ◽  
A. Toselli
Keyword(s):  
Boundary Layer ◽  
Discontinuous Galerkin ◽  
Incompressible Flow ◽  
Discontinuous Galerkin Methods ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Stability Result ◽  
Approximation Order ◽  
Galerkin Methods ◽  
Aspect Ratios

We consider stabilized mixed hp-discontinuous Galerkin methods for the discretization of the Stokes problem in three-dimensional polyhedral domains. The methods are stabilized with a term penalizing the pressure jumps. For this approach it is shown that ℚk-ℚk and ℚk-ℚk-1 elements satisfy a generalized inf–sup condition on geometric edge and boundary layer meshes that are refined anisotropically and non quasi-uniformly towards faces, edges, and corners. The discrete inf–sup constant is proven to be independent of the aspect ratios of the anisotropic elements and to decrease as k-1/2 with the approximation order. We also show that the generalized inf–sup condition leads to a global stability result in a suitable energy norm.

scholarly journals Hermite Type Spline Spaces over Rectangular Meshes with Complex Topological Structures

2017 ◽  
Vol 21 (3) ◽  
pp. 835-866 ◽  
Author(s):  
Meng Wu ◽  
Bernard Mourrain ◽  
André Galligo ◽  
Boniface Nkonga
Keyword(s):  
Isogeometric Analysis ◽  
Convergence Rates ◽  
Approximation Order ◽  
Basis Functions ◽  
Physical Domain ◽  
Piecewise Polynomial ◽  
Numerical Convergence ◽  
Rectangular Mesh ◽  
Piecewise Polynomial Functions ◽  
Potential Applications

AbstractMotivated by the magneto hydrodynamic (MHD) simulation for Tokamaks with Isogeometric analysis, we present splines defined over a rectangular mesh with a complex topological structure, i.e., with extraordinary vertices. These splines are piecewise polynomial functions of bi-degree (d,d) and parameter continuity. And we compute their dimension and exhibit basis functions called Hermite bases for bicubic spline spaces. We investigate their potential applications for solving partial differential equations (PDEs) over a physical domain in the framework of Isogeometric analysis. For instance, we analyze the property of approximation of these spline spaces for the L2-norm; we show that the optimal approximation order and numerical convergence rates are reached by setting a proper parameterization, although the fact that the basis functions are singular at extraordinary vertices.

HIGH APPROXIMATION ORDER BIORTHOGONAL MULTISCALING FUNCTIONS WITH DILATION FACTOR a

2010 ◽  
Vol 08 (06) ◽  
pp. 895-903 ◽  
Author(s):  
CHANGZHEN XIE
Keyword(s):  
Approximation Order ◽  
High Approximation ◽  
Dilation Factor ◽  
High Approximation Order ◽  
Special Case ◽  
Multiscaling Function

An algorithm is presented for constructing a pair of high approximation order biorthogonal multiscaling function with dilation factor a in terms of any given pair of biorthogonal multiscaling function. The special case that a = 2 is discussed. If the dilation factor a = 2, then a biorthogonal multiwavelet pair is constructed explicitly. Finally, examples are given.

On the enhancement of the approximation order of triangular Shepard method

2016 ◽  
Author(s):  
Francesco Dell’Accio ◽  
Filomena Di Tommaso ◽  
Kai Hormann
Keyword(s):  
Approximation Order
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