The role of boundary conditions on convergence properties of peridynamic model for transient heat transfer

DOI10.1007/s10915-021-01469-0zbMath1464.80005OpenAlexW3147206628MaRDI QIDQ2025866

Zian Liu, Jiangming Zhao, Xuhao Peng, Tie Mei, Zi-Guang Chen, Florin Bobaru

Publication date: 17 May 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-021-01469-0

zbMATH Keywords

convergenceboundary conditionstransient diffusionnonlocal diffusionperidynamicsasymptotically compatible scheme

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theories of fracture and damage (74A45) Numerical quadrature and cubature formulas (65D32) Finite difference methods applied to problems in thermodynamics and heat transfer (80M20) Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer (80M10) PDEs in connection with classical thermodynamics and heat transfer (35Q79) Integro-partial differential equations (35R09) Diffusive and convective heat and mass transfer, heat flow (80A19)

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Cites Work

• Unnamed Item
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• Mesh sensitivity in peridynamic simulations
• A peridynamic formulation of pressure driven convective fluid transport in porous media
• Peridynamic thermal diffusion
• A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities
• The peridynamic formulation for transient heat conduction
• Equations on transfer in nonlocal media
• Nonlocal thermoelasticity based on nonlocal heat conduction and nonlocal elasticity
• Reformulation of elasticity theory for discontinuities and long-range forces
• Surface corrections for peridynamic models in elasticity and fracture
• An energy-based coupling approach to nonlocal interface problems
• A constructive peridynamic kernel for elasticity
• Peridynamic states and constitutive modeling
• Finite propagation speed for limited flux diffusion equations
• Asymptotically Compatible Schemes and Applications to Robust Discretization of Nonlocal Models
• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Analysis and Comparison of Different Approximations to Nonlocal Diffusion and Linear Peridynamic Equations