A Petrov–Galerkin RBF method for diffusion equation on the unit sphere

DOI10.1002/num.22498OpenAlexW3043390144WikidataQ114235283 ScholiaQ114235283MaRDI QIDQ6088419

Davoud Mirzaei, Mohammadreza Ahmadi Darani

Publication date: 14 December 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.22498

zbMATH Keywords

radial basis functionsPetrov-Galerkin methodmeshless methodsspherical basis functionsdiffusion on the sphere

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiscale RBF collocation for solving PDEs on spheres
• Numerical integration with polynomial exactness over a spherical cap
• Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
• Spherical harmonics and approximations on the unit sphere. An introduction
• Continuous and discrete least-squares approximation by radial basis functions on spheres
• Approximation power of RBFs and their associated SBFs: a connection
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• Distributing many points on a sphere
• Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
• A localized RBF-MLPG method for numerical study of heat and mass transfer equations in elliptic fins
• Direct approximation on spheres using generalized moving least squares
• Approximation of continuous surface differential operators with the generalized moving least-squares (GMLS) method for solving reaction-diffusion equation
• Galerkin approximation for elliptic PDEs on spheres
• Approximation of parabolic PDEs on spheres using spherical basis functions
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• A Duchon framework for the sphere
• Direct meshless local Petrov-Galerkin (DMLPG) method: A generalized MLS approximation
• A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres
• Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions
• Unsymmetric meshless methods for operator equations
• On analysis of kernel collocation methods for spherical PDEs
• Positive definite functions on spheres
• A novel Galerkin method for solving PDES on the sphere using highly localized kernel bases
• Scattered Data Interpolation on Embedded Submanifolds with Restricted Positive Definite Kernels: Sobolev Error Estimates
• Surfaces Generated by Moving Least Squares Methods
• Strictly Positive Definite Functions on Spheres
• Error estimates for scattered data interpolation on spheres
• Meshless Galerkin methods using radial basis functions
• Element‐free Galerkin methods
• Generalized Hermite Interpolation Via Matrix-Valued Conditionally Positive Definite Functions
• On a new condition for strictly positive definite functions on spheres
• A Petrov--Galerkin Kernel Approximation on the Sphere
• Strictly positive definite functions on spheres in Euclidean spaces
• Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
• A necessary and sufficient condition for strictly positive definite functions on spheres
• Convergent Overdetermined-RBF-MLPG for Solving Second Order Elliptic PDEs
• Scattered Data Approximation

This page was built for publication: A Petrov–Galerkin RBF method for diffusion equation on the unit sphere