Performance analyses of mesh-based local finite element method and meshless global RBF collocation method for solving Poisson and Stokes equations

DOI10.1016/j.matcom.2022.02.015OpenAlexW4213127264MaRDI QIDQ2139871

Ceren Gürkan, Cem Avcı, İsmet Karakan

Publication date: 19 May 2022

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2022.02.015

zbMATH Keywords

finite element methodelliptic problemscontinuous Galerkinradial basis function collocation methodcomparison analysis

Mathematics Subject Classification ID

Fluid mechanics (76-XX) Numerical analysis (65-XX)

Cites Work

• The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
• Comparison of local weak and strong form meshless methods for 2-D diffusion equation
• A comparison of the meshless RBF collocation method with finite element and boundary element methods in neutron diffusion calculations
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• A posteriori error estimators in the finite element method
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• The uniform convergence of thin plate spline interpolation in two dimensions
• Convergence error estimate in solving free boundary diffusion problem by radial basis functions method.
• A comparison of efficiency and error convergence of multiquadric collocation method and finite element method.
• The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics
• A new spectral meshless radial point interpolation (SMRPI) method: a well-behaved alternative to the meshless weak forms
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Shape preserving properties and convergence of univariate multiquadric quasi-interpolation
• Error estimates and condition numbers for radial basis function interpolation
• A comparison of three explicit local meshless methods using radial basis functions
• Meshless techniques for convection dominated problems
• A local integral equation formulation to solve coupled nonlinear reaction-diffusion equations by using moving least square approximation
• A meshfree method based on radial basis functions for the eigenvalues of transient Stokes equations
• A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
• Mixed and Hybrid Finite Element Methods
• Local error estimates for radial basis function interpolation of scattered data
• Multivariate Interpolation and Conditionally Positive Definite Functions. II
• The numerical solution of the Navier-Stokes equations for an incompressible fluid
• A meshless local Petrov-Galerkin (MLPG) method for free and forced vibration analyses for solids
• A local point interpolation method for static and dynamic analysis of thin beams
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