Numerical integration based on trivariate C 2 quartic spline quasi-interpolants

Dagnino, Catterina; Lamberti, Paola; Remogna, Sara

doi:10.1007/s10543-013-0431-7

Cited by 6 publications

(4 citation statements)

References 23 publications

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“…in ( 4), and ii) in choosing coefficient functionals based on QI knots lying inside or on ∂ , for which extra values outside the domain are not necessary. Therefore with such a new partition S 1 , S 2 and W 2 operators (see Table 1) are proposed, taking into account both boundary conditions [26] (see also [36] for 1D case) and the presence of multiple knots [43]. Moreover some computational aspects of their construction are presented in [34] and an error analysis for f and its derivatives is provided in [45], making a particular effort to give error bounds in terms of the smoothness of f and the characteristics of the triangulation, also in the case of functions that are not regular enough.…”

Section: Approximation Of Functions and Datamentioning

confidence: 99%

On spline quasi-interpolation through dimensions

Dagnino¹,

Lamberti²,

Remogna³

2022

Ann Univ Ferrara

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The approximation of functions and data in one and high dimensions is an important problem in many mathematical and scientific applications. Quasi-interpolation is a general and powerful approximation approach having many advantages. This paper deals with spline quasi-interpolants and its aim is to collect the main results obtained by the authors, also in collaboration with other researchers, in such a topic through spline dimension, i.e. in the 1D, 2D and 3D setting, highlighting the approximation properties and the reconstruction of functions and data, the applications in numerical integration and differentiation and the numerical solution of integral and differential problems.

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Section: Approximation Of Functions and Datamentioning

confidence: 99%

On spline quasi-interpolation through dimensions

Dagnino¹,

Lamberti²,

Remogna³

2022

Ann Univ Ferrara

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“…In [25] the problem of efficient evaluation of box splines is addressed by making use of the local Bernstein representation of basis functions on each triangle. Also, numerical integration schemes, which are important for applications, based on quasi-interpolation have been considered in [6,29]. Recent applications of box splines include surface fitting [23], and solving linear elasticity problems in isogeometric analysis [19].…”

Section: Introductionmentioning

confidence: 99%

Completeness characterization of Type-I box splines

Villamizar¹,

Mantzaflaris²,

Jüttler³

2020

Preprint

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We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. For any given Type-I box spline, of specific maximum degree and order of global smoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translates of box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain.

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“…Other methods based on trivariate C 1 splines of total degree have been proposed, in [16,29] and [25] on type-6 tetrahedral partitions, in [23] on truncated octahedral partitions, in [27,28,30] on Powell-Sabin (Worsey-Piper) split, and in [24] by using quadratic trivariate super splines on uniform tetrahedral partitions. Furthermore, higher smoothness C 2 has been considered in [10][11][12]18,20], where the reconstruction of volume data is provided in the space of C 2 quartic splines.…”

Section: Introductionmentioning

confidence: 99%