A meshless Galerkin method for non-local diffusion using localized kernel bases

DOI10.1090/mcom/3294zbMath1397.65277arXiv1601.02717OpenAlexW2963945004MaRDI QIDQ4640320

Stephen Rowe, Richard B. Lehoucq, Francis J. Narcowich, Joseph D. Ward

Publication date: 17 May 2018

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

Full work available at URL: https://arxiv.org/abs/1601.02717

zbMATH Keywords

convergenceradial basis functionsinf-sup conditionvolume constraintmeshless methodnon-local diffusionlocalized Lagrange bases

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Integral operators (45P05) Integral operators (47G10) Multidimensional problems (41A63) Approximation by other special function classes (41A30)

Related Items

Numerical methods for nonlocal and fractional models, A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations, Meshfree extrapolation with application to enhanced near-boundary approximation with local Lagrange kernels

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• The fractional Laplacian operator on bounded domains as a special case of the nonlocal diffusion operator
• Hitchhiker's guide to the fractional Sobolev spaces
• Radial basis functions for the solution of hypersingular operators on open surfaces
• On local RBF approximation
• Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions
• Linearized theory of peridynamic states
• A unified theory of radial basis functions. Native Hilbert spaces for radial basis functions. II
• A radial basis function Galerkin method for inhomogeneous nonlocal diffusion
• A novel Galerkin method for solving PDES on the sphere using highly localized kernel bases
• Localized Bases for Kernel Spaces on the Unit Sphere
• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• Results on Nonlocal Boundary Value Problems
• Survey of meshless and generalized finite element methods: A unified approach
• Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
• Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
• The Mathematical Theory of Finite Element Methods
• A Galerkin Radial Basis Function Method for Nonlocal Diffusion
• Scattered Data Approximation