Comparison of three meshless methods for 2D harmonic and biharmonic problems

DOI10.1016/j.enganabound.2020.04.003zbMath1464.65212OpenAlexW3036164835MaRDI QIDQ785183

Magdalena Mierzwiczak, Jan Adam Kołodziej

Publication date: 5 August 2020

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

Full work available at URL: https://doi.org/10.1016/j.enganabound.2020.04.003

zbMATH Keywords

meshless methodsmethod of fundamental solutionscollocation techniqueTrefftz method

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fundamental solutions, Green's function methods, etc. for boundary value problems involving PDEs (65N80)

Cites Work

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• Comparisons of fundamental solutions and particular solutions for Trefftz methods
• A modified collocation Trefftz method for the inverse Cauchy problem of Laplace equation
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• Boundary methods, c-complete systems for Stokes problems
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• Many names of the Trefftz method
• The method of fundamental solutions for the numerical solution of the biharmonic equation
• An effectively modified direct Trefftz method for 2D potential problems considering the domain's characteristic length
• Determination of the slip constant in the Beavers-Joseph experiment for laminar fluid flow through porous media using a meshless method
• On the equivalence of the Trefftz method and method of fundamental solutions for Laplace and biharmonic equations
• Comparison of different methods for choosing the collocation points in the boundary collocation method for 2D-harmonic problems with special purpose Trefftz functions
• A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length
• Connectivity as an alternative to boundary integral equations: Construction of bases
• The method of functional equations for the approximate solution of certain boundary value problems

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