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arXiv · 1607.05936

Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements

A. S. Dedner·C. Ortner·H. Wu
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Abstract

We formulate a patch test consistent atomistic-to-continuum coupling (a/c) scheme that employs a second-order (potentially higher-order) finite element method in the material bulk. We prove a sharp error estimate in the energy-norm, which demonstrates that this scheme is (quasi-)optimal amongst energy-based sharp-interface a/c schemes that employ the Cauchy--Born continuum model. Our analysis also shows that employing a higher-order continuum discretization does not yield qualitative improvements to the rate of convergence.

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A. S. Dedner, C. Ortner, H. Wu. 2016-07-20. Analysis of patch-test consistent atomistic-to-continuum coupling with higher-order finite elements. https://arxiv.org/abs/1607.05936

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