Meshless solution of a diffusion equation with parameter optimization and error analysis

DOI10.1016/j.enganabound.2007.10.002zbMath1244.76088OpenAlexW2029381983MaRDI QIDQ443294

Roman Trobec, Marjan Šterk

Publication date: 7 August 2012

Published in: Engineering Analysis with Boundary Elements (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.enganabound.2007.10.002

zbMATH Keywords

diffusion equationaccuracymoving least squaresparameter optimizationmeshless local Petrov-Galerkin methodmesh-free

Mathematics Subject Classification ID

Related Items (7)

A parametric study of the MLPG method for thermo-mechanical solidification analysis ⋮ On preconditioned BiCGSTAB solver for MLPG method applied to heat conduction in 3D complex geometry ⋮ Solution of a low Prandtl number natural convection benchmark by a local meshless method ⋮ Comparison of local weak and strong form meshless methods for 2-D diffusion equation ⋮ Simulation of macrosegregation with mesosegregates in binary metallic casts by a meshless method ⋮ Interpolating meshless local Petrov-Galerkin method for steady state heat conduction problem ⋮ Analysis of the MLS variants in the meshless local Petrov-Galerkin method for a solution to the 2D Laplace equation

Uses Software

• FEMLAB
• FEAPpv
• Mfree2D

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The three R's of engineering analysis and error estimation and adaptivity
• Generalizing the finite element method: Diffuse approximation and diffuse elements
• Error estimates for interpolation by compactly supported radial basis functions of minimal degree
• A local boundary integral equation (LBIE) method in computational mechanics, and a meshless discretization approach
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Meshless methods: An overview and recent developments
• An \(h\)-\(p\) adaptive method using clouds
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Large-scale application of some modern CSM methodologies by parallel computation
• Towards a mesh-free computation of transport phenomena
• Smoothed particle hydrodynamics: theory and application to non-spherical stars
• The finite difference method at arbitrary irregular grids and its application in applied mechanics
• Surfaces Generated by Moving Least Squares Methods
• Element‐free Galerkin methods
• THE PARTITION OF UNITY METHOD
• The meshless finite element method
• A mesh free approach using radial basis functions and parallel domain decomposition for solving three‐dimensional diffusion equations

This page was built for publication: Meshless solution of a diffusion equation with parameter optimization and error analysis