Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model

DOI10.1016/j.apnum.2022.11.015arXiv2010.09215OpenAlexW4309486626MaRDI QIDQ6101745

Xiaobo Yin, Jiankang Shi, Yingfan Qi, Rongjun Cao, Minghua Chen

Publication date: 20 June 2023

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09215

zbMATH Keywords

nonlocal modelstability and convergence analysisasymptotically compatible schemeshifted-symmetric collocation

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Numerical methods for partial differential equations, boundary value problems (65Nxx) Numerical methods for integral equations, integral transforms (65Rxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations
• A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation
• A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
• Fast and high-order accuracy numerical methods for time-dependent nonlocal problems in \(\mathbb{R}^2\)
• Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
• An accurate and asymptotically compatible collocation scheme for nonlocal diffusion problems
• A fast collocation method for a variable-coefficient nonlocal diffusion model
• Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
• Reformulation of elasticity theory for discontinuities and long-range forces
• Fractional diffusion on bounded domains
• A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation
• Error analysis of the Crank-Nicolson SAV method for the Allen-Cahn equation on variable grids
• Correction of high-order BDF convolution quadrature for fractional Feynman-Kac equation with Lévy flight
• A conservative nonlocal convection-diffusion model and asymptotically compatible finite difference discretization
• A conforming DG method for linear nonlocal models with integrable kernels
• Quadrature rules for finite element approximations of 1D nonlocal problems
• A radial basis function Galerkin method for inhomogeneous nonlocal diffusion
• Long Time Stability of High Order MultiStep Numerical Schemes for Two-Dimensional Incompressible Navier--Stokes Equations
• Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations
• Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
• Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations
• Johann Faulhaber and Sums of Powers
• The Numerical Solution of Integral Equations of the Second Kind
• Nonlocal Modeling, Analysis, and Computation
• The Exponential Accuracy of Fourier and Chebyshev Differencing Methods
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• A sharp error estimate of piecewise polynomial collocation for nonlocal problems with weakly singular kernels
• On the Convergence to Local Limit of Nonlocal Models with Approximated Interaction Neighborhoods
• Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation
• Asymptotically Compatible Reproducing Kernel Collocation and Meshfree Integration for Nonlocal Diffusion
• A <scp>Fourier</scp> pseudospectral method for the “good” <scp>Boussinesq</scp> equation with second‐order temporal accuracy
• Asymptotically Compatible Schemes for Robust Discretization of Parametrized Problems with Applications to Nonlocal Models
• Fourth Order Accurate Scheme for the Space Fractional Diffusion Equations
• Convergence Analysis of a Multigrid Method for a Nonlocal Model
• Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
• Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions
• Numerical methods for nonlocal and fractional models

This page was built for publication: Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model