2012
DOI: 10.1016/j.amc.2012.09.044
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Abstract: In several applications, such as WENO interpolation and reconstruction [Shu C.W.: SIAM Rev. 51 (2009) , we are interested in the analytical expression of the weight-functions which allow the representation of the approximating function on a given stencil (Chebyshev-system) as the weighted combination of the corresponding approximating functions on substencils (Chebyshev-subsystems). We show that the weight-functions in such representations [Mühlbach G.: Num. Math. 31 (1978) 97-110] can be generated by a gen… Show more

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Cited by 3 publications
(15 citation statements)
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References 11 publications
(41 reference statements)
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“…For both cases it is shown [6,11] that ∀ξ ∈ [−1, 1] the linear weights are positive, and as a consequence the above combination of substencils is convex ∀ξ ∈ [−1, 1]. In a recent work [12] we extended these results for the general K s -level subdivision of an arbitrary stencil X i−M − ,i+M + : [13] studies Chebyshev-systems satisfying interpolatory conditions. In the reconstructing polynomial case (5a), the usual linear system approach [10, (13) [12, (4e), Lemma 2.1], only requires that the (K s = 1)-level subdivision can be defined.…”
Section: Introductionmentioning
confidence: 78%
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“…For both cases it is shown [6,11] that ∀ξ ∈ [−1, 1] the linear weights are positive, and as a consequence the above combination of substencils is convex ∀ξ ∈ [−1, 1]. In a recent work [12] we extended these results for the general K s -level subdivision of an arbitrary stencil X i−M − ,i+M + : [13] studies Chebyshev-systems satisfying interpolatory conditions. In the reconstructing polynomial case (5a), the usual linear system approach [10, (13) [12, (4e), Lemma 2.1], only requires that the (K s = 1)-level subdivision can be defined.…”
Section: Introductionmentioning
confidence: 78%
“…The analytical results obtained in the present work, in particular the recursive analytical expression of the weightfunctions σ R 1 ,M − ,M + ,K s ,k s (ξ) (Proposition 4.5) and the factorization of the fundamental functions of Lagrange reconstruction α R 1 ,M − ,M + ,ℓ (ξ) (Proposition 3.7), can be used to study convexity intervals for arbitrary values of [M ± , K s ], as was recently done for the Lagrange interpolating polynomial [12,Proposition 3.2]. In [7, Result 6.1, p. 300] we had conjectured that for any choice of [M ± , K s ] for which all of the substencils S i,M − −k s ,M + −K s +k s (k s ∈ {0, · · · , K s }) contain either point i or point i + 1 (or both), convexity was observed at ξ = 1 2 .…”
Section: Convexitymentioning
confidence: 99%
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“…Correlations in (1b) were computed using order-4 inhomogeneous-grid interpolating polynomials (Gerolymos, 2012) and sampled at every iteration (∆t + s = ∆t + 0.0059) for an observation interval t + OBS 1113. Because of the relatively short observation interval, the pressure term Π εij (1b) which contains the highly intermittent pressure-Hessian (Vreman and Kuerten, 2014b, Fig.…”
Section: Dns Computationsmentioning
confidence: 99%