Error analysis of the meshless finite point method

DOI10.1016/j.amc.2020.125326OpenAlexW3023994696MaRDI QIDQ2185431

Haiyun Dong, Xiao-Lin Li

Publication date: 4 June 2020

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

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125326

zbMATH Keywords

error estimatescondition numbermeshless methodsmoving least squares approximationfinite point method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15)

Related Items (24)

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory ⋮ Meshless acoustic analysis using a weakly singular Burton-Miller boundary integral formulation ⋮ Theoretical analysis of the generalized finite difference method ⋮ Analysis of a superconvergent recursive moving least squares approximation ⋮ Analysis of the moving least squares approximation with smoothed gradients ⋮ Localized method of fundamental solutions for two-dimensional anisotropic elasticity problems ⋮ Analysis of the element-free Galerkin method with penalty for general second-order elliptic problems ⋮ An improved meshless method based on the dimension splitting moving least-squares method for elasticity problems ⋮ A meshless finite point method for the improved Boussinesq equation using stabilized moving least squares approximation and Richardson extrapolation ⋮ The element‐free Galerkin method for a quasistatic contact problem with the Tresca friction in elastic materials ⋮ Optimal uniform error estimates for moving <scp>least‐squares</scp> collocation with application to option pricing under jump‐diffusion processes ⋮ Application of direct meshless local <scp>Petrov–Galerkin</scp> method for numerical solution of stochastic elliptic interface problems ⋮ On the augmented moving least squares approximation and the localized method of fundamental solutions for anisotropic heat conduction problems ⋮ An element-free Galerkin method for the obstacle problem ⋮ Unnamed Item ⋮ A divergence-free generalized moving least squares approximation with its application ⋮ Integrating Krylov Deferred Correction and Generalized Finite Difference Methods for Dynamic Simulations of Wave Propagation Phenomena in Long-Time Intervals ⋮ The elastoplastic analysis of functionally graded materials using a meshfree RRKPM ⋮ A spatial-temporal GFDM with an additional condition for transient heat conduction analysis of FGMs ⋮ An efficient localized meshless technique for approximating nonlinear sinh-Gordon equation arising in surface theory ⋮ A finite point method for the fractional cable equation using meshless smoothed gradients ⋮ A GFDM with supplementary nodes for thin elastic plate bending analysis under dynamic loading ⋮ A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS ⋮ A high-efficient splitting step reduced-dimension pure meshless method for transient 2D/3D Maxwell's equations in complex irregular domain

Cites Work

• Unnamed Item
• On the stability of the moving least squares approximation and the element-free Galerkin method
• Positivity conditions in meshless collocation methods
• Error estimates for the moving least-square approximation and the element-free Galerkin method in \(n\)-dimensional spaces
• Error estimates for the finite point method
• The generalized finite point method
• A stabilized finite point method for analysis of fluid mechanics problems
• Comparative accuracy and performance assessment of the finite point method in compressible flow problems
• A-posteriori error estimation for the finite point method with applications to compressible flow
• Analyzing wave propagation problems with the improved complex variable element-free Galerkin method
• The meshless finite point method for transient elastodynamic problems
• Variational multiscale interpolating element-free Galerkin method for the nonlinear Darcy-Forchheimer model
• Analysis of the element-free Galerkin method for Signorini problems
• Analysis of an augmented moving least squares approximation and the associated localized method of fundamental solutions
• Three-dimensional complex variable element-free Galerkin method
• Local Dirichlet-type absorbing boundary conditions for transient elastic wave propagation problems
• The interpolating element-free Galerkin (IEFG) method for three-dimensional potential problems
• A complex variable boundary element-free method for the Helmholtz equation using regularized combined field integral equations
• The improved element-free Galerkin method for three-dimensional elastoplasticity problems
• Simple modifications for stabilization of the finite point method
• A Finite Point Method Based on Directional Differences
• A FINITE POINT METHOD IN COMPUTATIONAL MECHANICS. APPLICATIONS TO CONVECTIVE TRANSPORT AND FLUID FLOW
• Equilibrium on line method (ELM) for imposition of Neumann boundary conditions in the finite point method (FPM)

This page was built for publication: Error analysis of the meshless finite point method