Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds

DOI10.1007/978-3-319-72456-0_24zbMath1405.41009arXiv1406.1435OpenAlexW2752152765MaRDI QIDQ4611815

Thomas Hangelbroek, Christian Rieger, Francis J. Narcowich, Joseph D. Ward

Publication date: 22 January 2019

Published in: Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1435

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Global Riemannian geometry, including pinching (53C20) Inverse theorems in approximation theory (41A27)

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A Kernel-Based Least-Squares Collocation Method for Surface Diffusion, Error bounds for a least squares meshless finite difference method on closed manifolds, A Kernel-Based Embedding Method and Convergence Analysis for Surfaces PDEs, Meshfree extrapolation with application to enhanced near-boundary approximation with local Lagrange kernels, An inverse theorem for compact Lipschitz regions in ℝ^{𝕕} using localized kernel bases, A meshless Galerkin method for non-local diffusion using localized kernel bases, Extrinsic Meshless Collocation Methods for PDEs on Manifolds

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