A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
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Publication:3015036
DOI10.1090/S0025-5718-2010-02453-6zbMath1387.74006arXiv0911.0671MaRDI QIDQ3015036
Publication date: 8 July 2011
Published in: Mathematics of Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0911.0671
Numerical approximation of solutions of equilibrium problems in solid mechanics (74G15) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Molecular, statistical, and kinetic theories in solid mechanics (74A25)
Related Items (19)
A Posteriori Error Estimation and Adaptive Algorithm for Atomistic/Continuum Coupling in Two Dimensions ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ A Framework for a Generalization Analysis of Machine-Learned Interatomic Potentials ⋮ Efficient a posteriori error control of a concurrent multiscale method with sharp interface for crystalline defects ⋮ QM/MM Methods for Crystalline Defects. Part 3: Machine-Learned MM Models ⋮ A theoretical case study of the generalization of machine-learned potentials ⋮ Finite element analysis of Cauchy-Born approximations to atomistic models ⋮ Stability of the minimum energy path ⋮ A priori error analysis of two force-based atomistic/continuum models of a periodic chain ⋮ 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 ⋮ Analysis of Geometrically Consistent Schemes with Finite Range Interaction ⋮ 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 ⋮ Analysis of a Predictor-Corrector Method for Computationally Efficient Modeling of Surface Effects in 1D ⋮ Theory-based benchmarking of the blended force-based quasicontinuum method ⋮ Energy minimization of two dimensional incommensurate heterostructures ⋮ A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods ⋮ (In-)stability and Stabilization of QNL-Type Atomistic-to-Continuum Coupling Methods
Cites Work
- Accuracy of quasicontinuum approximations near instabilities
- Cauchy-Born rule and the stability of crystalline solids: Static problems
- Stability, instability, and error of the force-based quasicontinuum approximation
- An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
- Cauchy-Born rule and the stability of crystalline solids: dynamic problems
- Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model
- Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation
- A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
- Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
- An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
- A Posteriori Existence in Numerical Computations
- An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method
- Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel–Kontorova Model
- Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
- Analysis of a quasicontinuum method in one dimension
- Analysis of a force-based quasicontinuum approximation
- Convergence Analysis of a Quasi‐Continuum Approximation for a Two‐Dimensional Material Without Defects
- Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics
- Computer-assisted enclosure methods for elliptic differential equations
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