Convergence and error estimates for meshless Galerkin methods

DOI10.1016/j.amc.2006.05.194zbMath1118.65115OpenAlexW1986620407MaRDI QIDQ879570

Zhi-Jie Cai

Publication date: 14 May 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.05.194

zbMATH Keywords

convergenceDirichlet problemerror estimatesfinite element methodnumerical examplesradial basis functionmeshless method

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)

Related Items (11)

Error analysis of an implicit Galerkin meshfree scheme for general second-order parabolic problems ⋮ Analysis of the element free Galerkin (EFG) method for solving fractional cable equation with Dirichlet boundary condition ⋮ Numerical solution of fractional partial differential equations by using radial basis functions combined with Legendre wavelets ⋮ Analysis of a meshless method for the time fractional diffusion-wave equation ⋮ An implicit RBF meshless approach for solving the time fractional nonlinear sine-Gordon and Klein-Gordon equations ⋮ Numerical investigation of reproducing kernel particle Galerkin method for solving fractional modified distributed-order anomalous sub-diffusion equation with error estimation ⋮ Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems ⋮ Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method ⋮ ℋ︁‐matrix preconditioners for symmetric saddle‐point systems from meshfree discretization ⋮ Best estimates of RBF-based meshless Galerkin methods for Dirichlet problem ⋮ MESHLESS GALERKIN METHOD BASED ON RBFS AND REPRODUCING KERNEL FOR QUASI-LINEAR PARABOLIC EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

Cites Work

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• Convergence order estimates of meshless collocation methods using radial basis functions
• Error estimates for interpolation by compactly supported radial basis functions of minimal degree
• Meshless Galerkin method based on regions partitioned into subdomains
• Operators on radial functions
• Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
• Approximation by radial basis functions with finitely many centers
• Some recent results and proposals for the use of radial basis functions in the BEM
• Solving differential equations with radial basis functions: Multilevel methods and smoothing
• Local error estimates for radial basis function interpolation of scattered data
• Meshless Galerkin methods using radial basis functions

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