A numerical study of divergence-free kernel approximations

Arthur A. Mitrano, Rodrigo Platte

Research output: Contribution to journalArticle

Abstract

Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.

Original languageEnglish (US)
Pages (from-to)94-107
Number of pages14
JournalApplied Numerical Mathematics
Volume96
DOIs
StatePublished - May 30 2015

Fingerprint

Divergence-free
Interpolants
Numerical Study
Vector Field
Divergence-free Vector Fields
kernel
Lebesgue Constant
Numerical Results
Multivariate Polynomials
Approximation Property
Approximation
Divergence
Rate of Convergence
Grid
Derivative
Three-dimensional
Vertex of a graph
Operator
Polynomials
Derivatives

Keywords

  • Divergence-free
  • Finite-differences
  • Radial basis functions
  • Spectral methods

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

A numerical study of divergence-free kernel approximations. / Mitrano, Arthur A.; Platte, Rodrigo.

In: Applied Numerical Mathematics, Vol. 96, 30.05.2015, p. 94-107.

Research output: Contribution to journalArticle

@article{bdce3500daec4906ada885f5ba8d1fbf,
title = "A numerical study of divergence-free kernel approximations",
abstract = "Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.",
keywords = "Divergence-free, Finite-differences, Radial basis functions, Spectral methods",
author = "Mitrano, {Arthur A.} and Rodrigo Platte",
year = "2015",
month = "5",
day = "30",
doi = "10.1016/j.apnum.2015.05.001",
language = "English (US)",
volume = "96",
pages = "94--107",
journal = "Applied Numerical Mathematics",
issn = "0168-9274",
publisher = "Elsevier",

}

TY - JOUR

T1 - A numerical study of divergence-free kernel approximations

AU - Mitrano, Arthur A.

AU - Platte, Rodrigo

PY - 2015/5/30

Y1 - 2015/5/30

N2 - Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.

AB - Approximation properties of divergence-free vector fields by global and local solenoidal bases are studied. A comparison between interpolants generated with radial kernels and multivariate polynomials is presented. Numerical results show higher rates of convergence for derivatives of the vector field being approximated in directions enforced by the divergence operator when a rectangular grid is used. We also compute the growth of Lebesgue constants for uniform and clustered nodes and study the flat limit of divergence-free interpolants based on radial kernels. Numerical results are presented for two- and three-dimensional vector fields.

KW - Divergence-free

KW - Finite-differences

KW - Radial basis functions

KW - Spectral methods

UR - http://www.scopus.com/inward/record.url?scp=84930617881&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930617881&partnerID=8YFLogxK

U2 - 10.1016/j.apnum.2015.05.001

DO - 10.1016/j.apnum.2015.05.001

M3 - Article

AN - SCOPUS:84930617881

VL - 96

SP - 94

EP - 107

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

ER -