Recovery of high order accuracy in radial basis function approximations of discontinuous problems

DOI10.1007/s10915-010-9360-7zbMath1203.41011OpenAlexW2050136515MaRDI QIDQ618636

Sigal Gottlieb, Chris L. Bresten, Daniel Higgs, Jae-Hun Jung, Saeja Oh Kim

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-010-9360-7

zbMATH Keywords

radial basis functionsGibbs phenomenonpost-processingdiscontinuous problemsgegenbauer reconstruction methodGibbs complimentary

Mathematics Subject Classification ID

Numerical methods for trigonometric approximation and interpolation (65T40) Approximation by other special function classes (41A30)

Related Items (6)

A new class of high-order methods for fluid dynamics simulations using Gaussian process modeling: one-dimensional case ⋮ Recovering exponential accuracy in Fourier spectral methods involving piecewise smooth functions with unbounded derivative singularities ⋮ Stable reconstructions in Hilbert spaces and the resolution of the Gibbs phenomenon ⋮ Optimal approximation of infinite-dimensional holomorphic functions ⋮ Spectral collocation and radial basis function methods for one-dimensional interface problems ⋮ A new class of adaptive high-order targeted ENO schemes for hyperbolic conservation laws

Cites Work

• A numerical study of some radial basis function based solution methods for elliptic PDEs
• Parameter optimization and reduction of round off error for the Gegenbauer reconstruction method
• Robust reprojection methods for the resolution of the Gibbs phenomenon
• A note on the Gibbs phenomenon with multiquadric radial basis functions
• An iterative adaptive multiquadric radial basis function method for the detection of local jump discontinuities
• On the Gibbs phenomenon. I: Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function
• Improved accuracy of multiquadric interpolation using variable shape parameters
• Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations
• Adaptive radial basis function methods for time dependent partial differential equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• On the Gibbs phenomenon. V: Recovering exponential accuracy from collocation point values of a piecewise analytic function
• A note on the accuracy of spectral method applied to nonlinear conservation laws
• Recovering high-order accuracy in WENO computations of steady-state hyperbolic systems
• Transport schemes on a sphere using radial basis functions
• Adaptive residual subsampling methods for radial basis function interpolation and collocation problems
• Spectral Methods for Time-Dependent Problems
• On the Gibbs Phenomenon and Its Resolution
• Radial Basis Functions
• On the Gibbs Phenomenon IV: Recovering Exponential Accuracy in a Subinterval from a Gegenbauer Partial Sum of a Piecewise Analytic Function
• A numerical study of the accuracy and stability of symmetric and asymmetric RBF collocation methods for hyperbolic PDEs
• Polynomials and Potential Theory for Gaussian Radial Basis Function Interpolation
• The Solution of Algebraic and Transcendental Equations by Iteration

This page was built for publication: Recovery of high order accuracy in radial basis function approximations of discontinuous problems