A Priori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain
نویسندگان
چکیده
We derive a priori error estimates for three prototypical energy-based quasicontinuum (QC) methods: the local QC method, the energy-based QC method, and the quasinonlocal QC method. Our analysis clearly decomposes the consistency error into modelling and coarsening errors. While previous results on estimating the modelling error exist, we give a new and simpler proof based on negative-norm estimates. Our stability analysis extends the sharp estimates in [6] to the nonlinear setting. Finally, we present numerical experiments to illustrate the results of our analysis.
منابع مشابه
A priori and a posteriori analysis of the quasinonlocal quasicontinuum method in 1D
For a next-nearest neighbour pair interaction model in a periodic domain, a priori and a posteriori analyses of the quasinonlocal quasicontinuum method (QNL-QC) are presented. The results are valid for large deformations and essentially guarantee a one-to-one correspondence between atomistic solutions and QNL-QC solutions. The analysis is based on truncation error and residual estimates in nega...
متن کاملOptimal order finite element approximation for a hyperbolic integro-differential equation
Semidiscrete finite element approximation of a hyperbolic type integro-differential equation is studied. The model problem is treated as the wave equation which is perturbed with a memory term. Stability estimates are obtained for a slightly more general problem. These, based on energy method, are used to prove optimal order a priori error estimates.
متن کاملA Priori Error Analysis of Two Force-Based Atomistic/Continuum Hybrid Models of a Periodic Chain
The force-based quasicontinuum (QCF) approximation is a non-conservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a ...
متن کاملAn Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the quasi-nonlocal quasicontinuum approximation. For simplicity, the analysis is restricted to the case of second-neighbor interactions and is linearized about a uniforml...
متن کاملA priori error analysis of two force-based atomistic/continuum models of a periodic chain
The force-based quasicontinuum (QCF) approximation is a nonconservative atomistic/continuum hybrid model for the simulation of defects in crystals. We present an a priori error analysis of the QCF method, applied to a one-dimensional periodic chain, that is valid for an arbitrary interaction range, large deformations, and takes coarse-graining into account. Our main tool in this analysis is a n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010