A high-order meshless linearly implicit energy-preserving method for nonlinear wave equations on Riemannian manifolds
type: Item
instance of: scholarly article
title: A high-order meshless linearly implicit energy-preserving method for nonlinear wave equations on Riemannian manifolds
author: Zhengjie Sun
author: L. Ling
published in: SIAM Journal on Scientific Computing
publication date: 2024-12-20T00:00:00Z
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65D12
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 35R01
zbMATH DE Number: 7959776
zbMATH Keywords: radial basis function
zbMATH Keywords: positive definite functions
zbMATH Keywords: Lagrange basis functions
zbMATH Keywords: scalar auxiliary variable
zbMATH Keywords: energy conservation law
MaRDI profile type: Publication
cites work: Error Estimates for Finite Element Methods for Second Order Hyperbolic Equations
cites work: Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds
cites work: Hamiltonian Boundary Value Methods (Energy Conserving Discrete Line Integral Methods)
cites work: A note on the efficient implementation of Hamiltonian BVMs
cites work: Structure-preserving algorithms for the two-dimensional sine-Gordon equation with Neumann boundary conditions
cites work: Conserved quantities of some Hamiltonian wave equations after full discretization
cites work: Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field'' method
cites work: A Kernel-Based Least-Squares Collocation Method for Surface Diffusion
cites work: Extrinsic Meshless Collocation Methods for PDEs on Manifolds
cites work: Über die partiellen Differenzengleichungen der mathematischen Physik.
cites work: Quasi-linear perturbations of Hamiltonian Klein-Gordon equations on spheres
cites work: Q5693348
cites work: Second-order SAV schemes for the nonlinear Schrödinger equation and their error analysis
cites work: $L^2 $-Estimates for Galerkin Methods for Second Order Hyperbolic Equations
cites work: Symplectic Geometric Algorithms for Hamiltonian Systems
cites work: High-order Mass- and Energy-conserving SAV-Gauss Collocation Finite Element Methods for the Nonlinear Schrödinger Equation
cites work: Kernel based quadrature on spheres and other homogeneous spaces
cites work: Scattered data interpolation on embedded submanifolds with restricted positive definite kernels: Sobolev error estimates
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: Geometric Numerical Integration
cites work: Direct and Inverse Results on Bounded Domains for Meshless Methods via Localized Bases on Manifolds
cites work: Kernel Approximation on Manifolds II: The $L_{\infty}$ Norm of the $L_2$ Projector
cites work: Kernel Approximation on Manifolds I: Bounding the Lebesgue Constant
cites work: The design of conservative finite element discretisations for the vectorial modified KdV equation
cites work: A posteriori error estimates for discontinuous Galerkin methods for the generalized Korteweg-de Vries equation
cites work: A high-order meshless Galerkin method for semilinear parabolic equations on spheres
cites work: Linearly implicit and high-order energy-conserving schemes for nonlinear wave equations
cites work: Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
cites work: Energy stability and convergence of SAV block-centered finite difference method for gradient flows
cites work: Geometric integration using discrete gradients
cites work: A novel Galerkin method for solving PDEs on the sphere using highly localized kernel bases
cites work: A Simple Mesh Generator in MATLAB
cites work: Numerical quadrature over smooth, closed surfaces
cites work: Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
cites work: Numerical analysis and simulation for a nonlinear wave equation
cites work: A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds
cites work: On Multiscale Quasi-Interpolation of Scattered Scalar- and Manifold-Valued Functions
cites work: Order-Preserving Approximations to Successive Derivatives of Periodic Functions by Iterated Splines
cites work: The scalar auxiliary variable (SAV) approach for gradient flows
cites work: A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
cites work: A Kernel-Based Meshless Conservative Galerkin Method for Solving Hamiltonian Wave Equations
cites work: Solving partial differential equations on (evolving) surfaces with radial basis functions
cites work: A Conservative Finite Element Method for the Korteweg-de Vries Equation
cites work: MGM: A Meshfree Geometric Multilevel Method for Systems Arising from Elliptic Equations on Point Cloud Surfaces
cites work: A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system
cites work: Symplectic wavelet collocation method for Hamiltonian wave equations
DOI: 10.1137/24M1654245
description: scientific article; zbMATH DE number 7959776