Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model

DOI10.1090/S0025-5718-02-01456-4zbMath1010.74003OpenAlexW2042069254MaRDI QIDQ4794634

Ping Lin

Publication date: 19 February 2003

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-02-01456-4

zbMATH Keywords

finite element methoderror estimationone-dimensional modelill-posednessLennard-Jones potentialglobal minimizationnearest neighbor interactionlattice staticsquasi-continuum approximationfull interactionatomistic-continuum approximationmaterial particle model

Mathematics Subject Classification ID

Related Items (19)

A PRIORI ERROR ESTIMATES FOR ENERGY-BASED QUASICONTINUUM APPROXIMATIONS OF A PERIODIC CHAIN ⋮ A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods ⋮ Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model ⋮ Accuracy of quasicontinuum approximations near instabilities ⋮ An efficient multigrid strategy for large-scale molecular mechanics optimization ⋮ Iterative solution of the quasicontinuum equilibrium equations with continuation ⋮ A Fast Front-Tracking Approach and Its Analysis for a Temporal Multiscale Flow Problem with a Fractional Order Boundary Growth ⋮ Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems ⋮ 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 ⋮ Stability, instability, and error of the force-based quasicontinuum approximation ⋮ Analysis of a quasicontinuum method in one dimension ⋮ Analysis of a force-based quasicontinuum approximation ⋮ Atomistic to Continuum limits for computational materials science ⋮ Finite-temperature coarse-graining of one-dimensional models: mathematical analysis and computational approaches ⋮ A note on the regularity of reduced models obtained by nonlocal quasi-continuum-like approaches ⋮ Analysis of an atomistic model for anti-plane fracture ⋮ An analysis of the effect of ghost force oscillation on quasicontinuum error ⋮ A Study on the Quasi-continuum Approximations of a One-Dimensional Fracture Model

Cites Work

• Elastic media with microstructure. I: One-dimensional models. (Transl. from the Russian)
• One-dimensional dislocations. I. Static theory
• Unnamed Item
• Unnamed Item

This page was built for publication: Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model