Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions
type: Item
instance of: scholarly article
title: Numerical simulation and error estimation of the time-dependent Allen-Cahn equation on surfaces with radial basis functions
zbMATH Open document ID: 1426.65149
author: Vahid Mohammadi
author: Davoud Mirzaei
author: Mehdi Dehghan
published in: Journal of Scientific Computing
publication date: 2019-06-27T00:00:00Z
review text: Well-known radial basis function methods are used to discretise the Allen-Cahn equation on surfaces in \(\mathbb{R}^3\) without boundary, together with a first-order splitting technique in time. An error analysis based on a conjecture is presented. Additionally, results of some numerical experiments are shown.
reviewed by: Hendrik Ranocha
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
zbMATH DE Number: 7074534
zbMATH Keywords: Allen-Cahn equation
zbMATH Keywords: radial basis functions
zbMATH Keywords: Laplace-Beltrami operator
zbMATH Keywords: time splitting scheme
zbMATH Keywords: error estimate
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: s10915-018-0859-7
OpenAlex ID: W2898360446
cites work: Transport and diffusion of material quantities on propagating interfaces via level set methods.
cites work: An extension of a bound for functions in Sobolev spaces, with applications to \((m, s)\)-spline interpolation and smoothing
cites work: Extension of sampling inequalities to Sobolev semi-norms of fractional order and derivative data
cites work: Geometrical image segmentation by the Allen-Cahn equation
cites work: Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
cites work: Variational problems and partial differential equations on implicit surfaces
cites work: A Finite Volume Method for Solving Parabolic Equations on Logically Cartesian Curved Surface Meshes
cites work: An efficient algorithm for solving the phase field crystal model
cites work: Motion by mean curvature of curves on surfaces using the Allen-Cahn Equation
cites work: Error analysis of the numerical solution of split differential equations
cites work: Q3814727
cites work: Finite elements on evolving surfaces
cites work: Q3446085
cites work: A radial basis function method for the shallow water equations on a sphere
cites work: Transport schemes on a sphere using radial basis functions
cites work: A high-order kernel method for diffusion and reaction-diffusion equations on surfaces
cites work: Order-preserving derivative approximation with periodic radial basis functions
cites work: Scattered data interpolation on embedded submanifolds with restricted positive definite kernels: Sobolev error estimates
cites work: Color Image Segmentation by the Vector-Valued Allen–Cahn Phase-Field Model: A Multigrid Solution
cites work: A conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier
cites work: A finite difference method for a conservative Allen-Cahn equation on non-flat surfaces
cites work: On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
cites work: Continuous and discrete least-squares approximation by radial basis functions on spheres
cites work: Galerkin approximation for elliptic PDEs on spheres
cites work: Multiscale RBF collocation for solving PDEs on spheres
cites work: A Radial Basis Function (RBF) Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces
cites work: A simple and efficient finite difference method for the phase-field crystal equation on curved surfaces
cites work: Level set equations on surfaces via the closest point method
cites work: Direct approximation on spheres using generalized moving least squares
cites work: A Petrov--Galerkin Kernel Approximation on the Sphere
cites work: Error bounds for solving pseudodifferential equations on spheres by collocation with zonal kernels
cites work: Approximation power of RBFs and their associated SBFs: a connection
cites work: Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting
cites work: Scattered Data Interpolation on Spheres: Error Estimates and Locally Supported Basis Functions
cites work: A novel Galerkin method for solving PDEs on the sphere using highly localized kernel bases
cites work: A radial basis function (RBF)-finite difference (FD) method for diffusion and reaction-diffusion equations on surfaces
cites work: A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities
cites work: Metastable Bubble Solutions for the Allen-Cahn Equation with Mass Conservation
cites work: Scattered Data Approximation
cites work: Divergence-Free Kernel Methods for Approximating the Stokes Problem
cites work: Approximate interpolation with applications to selecting smoothing parameters
cites work: The stabilized semi-implicit finite element method for the surface Allen-Cahn equation
DOI: 10.1007/S10915-018-0859-7
description: scientific article; zbMATH DE number 7074534