Robust a posteriori stress analysis for quadrature collocation approximations of nonlocal models via nonlocal gradients
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- Type
- article
- Published
- 2016-10-01
- Cited by
- 22
- References
- 39
- Access
- Open access
- OpenAlex
- https://openalex.org/W2496193280
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:124012989
Keywords
Discretization, Superconvergence, Mathematics, Applied mathematics, Partial differential equation
References
- An Integrodifferential Model for Phase Transitions: Stationary Solutions in Higher Space Dimensions
- Lévy Processes and Stochastic Calculus
- A Nonlocal Strain Measure for Digital Image Correlation.
- Asymptotically Compatible Schemes for Peridynamics Based on Numerical Quadratures
- An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures
- The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity
- Peridynamics as an Upscaling of Molecular Dynamics
- Peridynamics for multiscale materials modeling
- Coupling of peridynamic theory and the finite element method
- Continuous and discontinuous finite element methods for a peridynamics model of mechanics
- Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations
- Force flux and the peridynamic stress tensor
- Convergence, adaptive refinement, and scaling in 1D peridynamics
- The peridynamic formulation for transient heat conduction
- Critical thresholds in flocking hydrodynamics with non-local alignment
- Reformulation of Elasticity Theory for Discontinuities and Long-Range Forces
- Nonlocal convection–diffusion problems and finite element approximations
- Local and global minimizers for a variational energy involving a fractional norm
- Mixed finite element methods—reduced and selective integration techniques: a unification of concepts
- Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
Cited by
- Analysis of a nonlocal-in-time parabolic equation
- Nonlocal diffusion and peridynamic models with Neumann type constraints and their numerical approximations
- A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization
- A Quasi-nonlocal Coupling Method for Nonlocal and Local Diffusion Models
- Asymptotically compatible schemes for space-time nonlocal diffusion equations
- Stability of Nonlocal Dirichlet Integrals and Implications for Peridynamic Correspondence Material Modeling
- Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions
- Nonlocal gradient operators with a nonspherical interaction neighborhood and their applications
- AN INVITATION TO NONLOCAL MODELING, ANALYSIS AND COMPUTATION
- Nonlocal Models with Heterogeneous Localization and Their Application to Seamless Local-Nonlocal Coupling
- Numerical methods for nonlocal and fractional models
- Nonlocal-in-time dynamics and crossover of diffusive regimes
- Analysis of Coarse-Grained Lattice Models and Connections to Nonlocal Interactions
- Stability of a Nonlocal Traffic Flow Model for Connected Vehicles
- A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems
- Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon
- A probabilistic scheme for semilinear nonlocal diffusion equations with volume constraints
- A review of peridynamic theory and nonlocal operators along with their computer implementations
- On the long-time behavior of the continuous and discrete solutions of a nonlocal Cahn-Hilliard type inpainting model
- A novel a posteriori error estimator for adaptive FEM of nonlocal diffusion problems and related convergence analysis
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