Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications

DOI10.1051/m2an/2019053zbMath1450.76031arXiv1903.06025OpenAlexW2970387355MaRDI QIDQ5110257

Hwi Lee, Qiang Du

Publication date: 18 May 2020

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.06025

zbMATH Keywords

stabilityconvergencelinear elasticityDirichlet integralHelmholtz decompositionFourier integralincompressible Stokes flow

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Stokes and related (Oseen, etc.) flows (76D07) Basic methods in fluid mechanics (76M99) Numerical and other methods in solid mechanics (74S99)

Related Items

A Nonlocal Stokes System with Volume Constraints, Numerical methods for nonlocal and fractional models, A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems, A new nonlocal calculus framework. Helmholtz decompositions, properties, and convergence for nonlocal operators in the limit of the vanishing horizon, On the solution of hyperbolic equations using the peridynamic differential operator, Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications, Non-local gradients in bounded domains motivated by continuum mechanics: fundamental theorem of calculus and embeddings, Unnamed Item, Towards a unified theory of fractional and nonlocal vector calculus, Optimization and learning with nonlocal calculus, Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition, Stability of a Nonlocal Traffic Flow Model for Connected Vehicles

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlocal diffusion and applications
• A nonlocal continuum model for biological aggregation
• Characterization of function spaces of vector fields and an application in nonlinear peridynamics
• Localization of nonlocal gradients in various topologies
• Analysis of a nonlocal-in-time parabolic equation
• The div-curl lemma for sequences whose divergence and curl are compact in \(W^{-1,1}\)
• A variational approach to the consistency of spectral clustering
• Force flux and the peridynamic stress tensor
• Fractional vector calculus and fractional Maxwell's equations
• Regularization techniques for numerical approximation of PDEs with singularities
• Fractional div-curl quantities and applications to nonlocal geometric equations
• \(\Gamma\)-convergence of graph Ginzburg-Landau functionals
• Reformulation of elasticity theory for discontinuities and long-range forces
• Fractional diffusion on bounded domains
• A graph discretization of the Laplace-Beltrami operator
• Mathematics of smoothed particle hydrodynamics: a study via nonlocal Stokes equations
• Random dispersal vs. non-local dispersal
• A doubly nonlocal Laplace operator and its connection to the classical Laplacian
• A conservative nonlocal convection-diffusion model and asymptotically compatible finite difference discretization
• Stability of peridynamic correspondence material models and their particle discretizations
• Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients
• The Dirichlet problem for nonlocal operators
• Diffusion maps
• Global existence for chemotaxis with finite sampling radius
• Mathematical analysis for the peridynamic nonlocal continuum theory
• NONLOCAL KORN-TYPE CHARACTERIZATION OF SOBOLEV VECTOR FIELDS
• Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
• On a inequality of Friedrichs.
• Nonlocal Operators with Applications to Image Processing
• On the validity of Friedrichs' inequalities.
• Can the Nonlocal Characterization of Sobolev Spaces by Bourgain et al. Be Useful for Solving Variational Problems?
• The Weighted Particle Method for Convection-Diffusion Equations. Part 1: The Case of an Isotropic Viscosity
• Smoothed particle hydrodynamics: theory and application to non-spherical stars
• Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling
• Asymptotically Compatible SPH-Like Particle Discretizations of One Dimensional Linear Advection Models
• Nonlocal Modeling, Analysis, and Computation
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
• Image Denoising Methods. A New Nonlocal Principle
• Quasi-nonlocal Coupling of Nonlocal Diffusions
• Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
• The bond-based peridynamic system with Dirichlet-type volume constraint
• On the Dirichlet problem for second-order elliptic integro-differential equations