A kernel-based discretisation method for first order partial differential equations

DOI10.1090/mcom/3265zbMath1394.65087arXiv1601.06142OpenAlexW2596129588MaRDI QIDQ4637577

Tobias Ramming, Holger Wendland

Publication date: 24 April 2018

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.06142

zbMATH Keywords

stabilityconvergencefirst-order PDFkernel-based Eulerian approachmeshfree semi-discrete approximation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Systems of nonlinear first-order PDEs (35F50)

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Cites Work

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• Review on computational methods for Lyapunov functions
• Multivariate interpolation with increasingly flat radial basis functions of finite smoothness
• Radial basis function interpolation in the limit of increasingly flat basis functions
• On the convergence of SPH method for scalar conservation laws with boundary conditions
• High order accurate vortex methods with explicit velocity kernels
• Univariate multiquadric approximation: Quasi-interpolation to scattered data
• Fourier analysis of the approximation power of principal shift-invariant spaces
• Construction techniques for highly accurate quasi-interpolation operators
• Interpolation in the limit of increasingly flat radial basis functions
• On quasi-interpolation with radial basis functions
• On quasi-interpolation by radial basis functions with scattered centres
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Pointwise approximation with quasi-interpolation by radial basis functions
• Limit problems for interpolation by analytic radial basis functions
• On the inversion of the Vandermonde matrix
• Vorticity and Incompressible Flow
• Smoothed Particle Hydrodynamics and Its Diverse Applications
• High Order Weighted Essentially Nonoscillatory Schemes for Convection Dominated Problems
• Convergence of Univariate Quasi-Interpolation Using Multiquadrics
• ON PARTICLE WEIGHTED METHODS AND SMOOTH PARTICLE HYDRODYNAMICS
• Approximation from Shift-Invariant Subspaces of L 2 (ℝ d )
• Convergence Analysis for a Class of High-Order Semi-Lagrangian Advection Schemes
• Convergence of high-order deterministic particle methods for the convection-diffusion equation
• Radial Basis Functions
• Convergence of SPH Method for Scalar Nonlinear Conservation Laws
• Fluid Mechanics and the SPH Method
• Semi-Lagrangian Approximation Schemes for Linear and Hamilton—Jacobi Equations
• Solution of Vandermonde systems of equations
• Theory and Applications of Smoothed Particle Hydrodynamics
• Scattered Data Approximation