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Volume 12, Issue 1
A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain

Hao Wang, Shaohui Liu & Feng Yang

DOI: 10.4208/nmtma.OA-2017-0094

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 233-264.

Published online: 2018-09

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  • 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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@Article{NMTMA-12-233, author = {Hao Wang, Shaohui Liu and Feng Yang}, title = {A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {1}, pages = {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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2017-0094}, url = {http://global-sci.org/intro/article_detail/nmtma/12699.html} }
TY - JOUR T1 - A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain AU - Hao Wang, Shaohui Liu & Feng Yang JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 233 EP - 264 PY - 2018 DA - 2018/09 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2017-0094 UR - https://global-sci.org/intro/article_detail/nmtma/12699.html KW - AB -

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.

Hao Wang, Shaohui Liu and Feng Yang. (2018). A Posteriori Error Control for Three Typical Force-Based Atomistic-to-Continuum Coupling Methods for an Atomistic Chain. Numerical Mathematics: Theory, Methods and Applications. 12 (1). 233-264. doi:10.4208/nmtma.OA-2017-0094
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