Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations
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Publication:1735443
DOI10.1016/j.amc.2017.01.061zbMath1411.74058OpenAlexW2591506055MaRDI QIDQ1735443
Yunzhe Tao, Xiaochuan Tian, Qiang Du
Publication date: 28 March 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2017.01.061
Integro-partial differential equations (45K05) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Theories of fracture and damage (74A45)
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Cites Work
- Unnamed Item
- Unnamed Item
- Characterization of function spaces of vector fields and an application in nonlinear peridynamics
- Analysis of the volume-constrained peridynamic Navier equation of linear elasticity
- Analysis of a scalar nonlocal peridynamic model with a sign changing kernel
- Nonlocal constrained value problems for a linear peridynamic Navier equation
- Nonlocal problems with Neumann boundary conditions
- Continuous and discontinuous finite element methods for a peridynamics model of mechanics
- A fast Galerkin method with efficient matrix assembly and storage for a peridynamic model
- Crack nucleation in a peridynamic solid
- An estimate in the spirit of Poincaré's inequality
- Integral approximations to classical diffusion and smoothed particle hydrodynamics
- Reformulation of elasticity theory for discontinuities and long-range forces
- Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients
- On Neumann and oblique derivatives boundary conditions for nonlocal elliptic equations
- Nonlocal convection-diffusion volume-constrained problems and jump processes
- Kinetics of phase transformations in the peridynamic formulation of continuum mechanics
- How to approximate the heat equation with Neumann boundary conditions by nonlocal diffusion problems
- A meshfree unification: reproducing kernel peridynamics
- Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
- Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions
- Results on Nonlocal Boundary Value Problems
- On Neumann type problems for nonlocal equations set in a half space
- On the variational limit of a class of nonlocal functionals related to peridynamics
- Convergence, adaptive refinement, and scaling in 1D peridynamics
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
- A NONLOCAL VECTOR CALCULUS, NONLOCAL VOLUME-CONSTRAINED PROBLEMS, AND NONLOCAL BALANCE LAWS
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
- The bond-based peridynamic system with Dirichlet-type volume constraint
- Trace Theorems for some Nonlocal Function Spaces with Heterogeneous Localization
- A two-dimensional peridynamic model for thin plates
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