On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines

Iske, Armin

doi:10.1007/978-3-0348-8067-1_8

Cited by 34 publications

(39 citation statements)

References 15 publications

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“…We can prove the scale invariance for the general case of polyharmonic splines, where our arguments rely on the scale invariance of their Lagrange basis functions in combination with the representation of the Lebesgue constant in (11). Proof (sketch): Following our work [11], we see that the reconstruction space…”

Section: Scale-invariance Of the Lebesgue Constantmentioning

confidence: 97%

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On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

Iske

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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This contribution discusses the construction of kernel-based adaptive particle methods for numerical flow simulation, where the finite volume particle method (FVPM) is used as a prototype. In the FVPM, scattered data approximation algorithms are required in the recovery step of the WENO reconstruction. We first show how kernel-based approximation schemes can be used in the recovery step of particle methods, where we give preference to the radial polyharmonic spline kernel. Then we discuss important aspects concerning the numerical stability and approximation behaviour of polyharmonic splines. Moreover, we propose customized coarsening and refinement rules for the adaptive resampling of the particles. Supporting numerical examples and comparisons with other radial kernels are provided.

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Section: Scale-invariance Of the Lebesgue Constantmentioning

confidence: 97%

“…We have generalized this result in [11] to polyharmonic splines to obtain arbitrary high local approximation orders. We can sketch the proof of this important result as follows.…”

Section: Definitionmentioning

confidence: 99%

On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

Iske

2013

Notes on Numerical Fluid Mechanics and Multidisciplinary Design

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“…For all K(A) > 1 there is some u * ∈ U S and an admissible solution vectorũ satisfying (15) such that…”

Section: Sharpnessmentioning

confidence: 99%

“…Examples are in [29] and in Section 8 below. See [15] for an early work on stability of interpolation by polyharmonic kernels, and [1] for an example of an advanced application.…”

Section: Approximations By Polyharmonic Kernelsmentioning

confidence: 99%

Error Analysis of Nodal Meshless Methods

Schaback

2017

Meshfree Methods for Partial Differential Equations VIII

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“….., , 2 1 de n variáveis independentes, assumindo 1 ≥ d (Iske, 2003). A interpolação desses dados dispersos deve satisfazer a seguinte condição:…”

Section: Interpolação Spline Poliharmônicaunclassified

Um Método Meshfree Adaptativo De Advecção Para Problemas De Fluxo Bifásico De Fluidos Incompressíveis E Imiscíveis Em Meios Porosos Heterogêneos Tridimensionais

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On the Approximation Order and Numerical Stability of Local Lagrange Interpolation by Polyharmonic Splines

Cited by 34 publications

References 15 publications

On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

On the Construction of Kernel-Based Adaptive Particle Methods in Numerical Flow Simulation

Error Analysis of Nodal Meshless Methods

Um Método Meshfree Adaptativo De Advecção Para Problemas De Fluxo Bifásico De Fluidos Incompressíveis E Imiscíveis Em Meios Porosos Heterogêneos Tridimensionais

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