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
From MaRDI portal
Publication:4643813
DOI10.1137/17M1118579zbMath1450.65138arXiv1702.04048OpenAlexW2802392666MaRDI QIDQ4643813
Publication date: 29 May 2018
Published in: Multiscale Modeling & Simulation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1702.04048
Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Statics (70C20)
Related Items (3)
Efficient a posteriori error control of a concurrent multiscale method with sharp interface for crystalline defects ⋮ Adaptive QM/MM coupling for crystalline defects ⋮ A Posteriori Error Estimates for Adaptive QM/MM Coupling Methods
Cites Work
- Unnamed Item
- Unnamed Item
- An adaptive strategy for the control of modeling error in two-dimensional atomic-to-continuum coupling simulations
- On the application of the Arlequin method to the coupling of particle and continuum models
- Energy-based atomistic-to-continuum coupling without ghost forces
- From molecular models to continuum mechanics
- An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
- Goal-oriented adaptive mesh refinement for the quasicontinuum approximation of a Frenkel-Kontorova model
- The role of the patch test in 2D atomistic-to-continuum coupling methods
- 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
- Analysis of an Averaging Operator for Atomic-to-Continuum Coupling Methods by the Arlequin Approach
- 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
- Modeling Materials
- An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
- Error Estimation and Atomistic-Continuum Adaptivity for the Quasicontinuum Approximation of a Frenkel–Kontorova Model
- Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
- A simple error estimator and adaptive procedure for practical engineerng analysis
- A Posteriori Error Analysis of Finite Element Solutions for One-Dimensional Problems
- Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
- Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
- A Convergent Adaptive Algorithm for Poisson’s Equation
- Construction and Sharp Consistency Estimates for Atomistic/Continuum Coupling Methods with General Interfaces: A Two-Dimensional Model Problem
- Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice
- Atomistic-to-continuum coupling
- Analysis of a quasicontinuum method in one dimension
- Convergence Analysis of a Quasi‐Continuum Approximation for a Two‐Dimensional Material Without Defects
- A posteriori error control for a quasi-continuum approximation of a periodic chain
This page was built for publication: 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
