A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain

A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain

Year:    2019

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 233–264

Abstract

We consider the problem of a posteriori error estimates and adaptivity for three typical force-based atomistic-to-continuum coupling methods. Combining the residual and the stability estimates, we derive computable a posteriori error estimators for the three methods in the energy norm and formulate adaptive algorithms using these estimators. Our numerical experiments show optimal convergence rates of these algorithms. The efficiency of the estimators is also demonstrated numerically.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.OA-2017-0094

Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 1 : pp. 233–264

Published online:    2019-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    32

Keywords:   

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