Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice

DOI10.1090/S0025-5718-2013-02687-7zbMath1276.82013arXiv1104.0311MaRDI QIDQ5326506

Christoph Ortner, Alexander V. Shapeev

Publication date: 6 August 2013

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.0311

zbMATH Keywords

atomistic modelscoarse grainingatomistic-to-continuum coupling

Mathematics Subject Classification ID

Related Items (21)

A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions ⋮ Analysis of blended atomistic/continuum hybrid methods ⋮ Analysis of boundary conditions for crystal defect atomistic simulations ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ Existence and stability of a screw dislocation under anti-plane deformation ⋮ Efficient a posteriori error control of a concurrent multiscale method with sharp interface for crystalline defects ⋮ Approximation of Crystalline Defects at Finite Temperature ⋮ Finite element analysis of Cauchy-Born approximations to atomistic models ⋮ Justification of the Cauchy-Born approximation of elastodynamics ⋮ Development of an Optimization-Based Atomistic-to-Continuum Coupling Method ⋮ Convergence of a Force-Based Hybrid Method in Three Dimensions ⋮ Analysis of the Residual-Type and the Gradient Recovery-Type a Posteriori Error Estimators for a Consistent Atomistic-to-Continuum Coupling Method in One-Dimension ⋮ Adaptive QM/MM coupling for crystalline defects ⋮ A Posteriori Error Estimate and Adaptive Mesh Refinement Algorithm for Atomistic/Continuum Coupling with Finite Range Interactions in Two Dimensions ⋮ QM/MM Methods for Crystalline Defects. Part 2: Consistent Energy and Force-Mixing ⋮ Atomistic/Continuum Blending with Ghost Force Correction ⋮ Analysis of an optimization-based atomistic-to-continuum coupling method for point defects ⋮ Theory-based benchmarking of the blended force-based quasicontinuum method ⋮ (In-)stability and Stabilization of QNL-Type Atomistic-to-Continuum Coupling Methods ⋮ A Study on the Quasi-continuum Approximations of a One-Dimensional Fracture Model ⋮ An Atomistic/Continuum Coupling Method Using Enriched Bases

Cites Work

• Unnamed Item
• Unnamed Item
• A field theoretical approach to the quasi-continuum method
• Accuracy of quasicontinuum approximations near instabilities
• A priori error analysis of two force-based atomistic/continuum models of a periodic chain
• A bridging domain method for coupling continua with molecular dynamics
• On an h-type mesh-refinement strategy based on minimization of interpolation errors
• Stability, instability, and error of the force-based quasicontinuum approximation
• An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
• Coupled atomistic--continuum simulations using arbitrary overlapping domains
• The role of the patch test in 2D atomistic-to-continuum coupling methods
• On the stability of Bravais lattices and their Cauchy–Born approximations
• A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
• A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN
• A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods
• Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
• Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in Three Dimensions
• A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
• On the Convergence of Adaptive Nonconforming Finite Element Methods for a Class of Convex Variational Problems
• An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
• Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
• Some Optimal Error Estimates for Piecewise Linear Finite Element Approximations
• Positive Definiteness of the Blended Force-Based Quasicontinuum Method
• Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice
• Best approximation property in the $W^1_{\infty }$ norm for finite element methods on graded meshes
• Analysis of a quasicontinuum method in one dimension
• One-dimensional dislocations. I. Static theory

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