Convergence of meshless Petrov-Galerkin method using radial basis functions

DOI10.1016/j.amc.2006.05.085zbMath1112.65105OpenAlexW2152382137MaRDI QIDQ864773

Yunxin Zhang

Publication date: 13 February 2007

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.085

zbMATH Keywords

convergencenumerical results

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

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Cites Work

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• Adaptive multiquadric collocation for boundary layer problems
• Circumventing the ill-conditioning problem with multiquadric radial basis functions: Applications to elliptic partial differential equations
• Adaptive greedy techniques for approximate solution of large RBF systems
• A meshless, integration-free, and boundary-only RBF technique
• A least-squares preconditioner for radial basis functions collocation methods
• Multizone decomposition for simulation of time-dependent problems using the multiquadratic scheme
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• On unsymmetric collocation by radial basis functions
• Overlapping domain decomposition method by radial basis functions
• Compactly supported positive definite radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Fast Solution of the Radial Basis Function Interpolation Equations: Domain Decomposition Methods
• Meshless Galerkin methods using radial basis functions
• Special Finite Element Methods for a Class of Second Order Elliptic Problems with Rough Coefficients
• THE PARTITION OF UNITY METHOD
• A new class of radial basis functions with compact support
• Domain decomposition for radial basis meshless methods
• Interpolation with variably scaled kernels