Journal
MATHEMATICS OF COMPUTATION
Volume 80, Issue 275, Pages 1265-1285Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2010-02453-6
Keywords
Quasicontinuum method; quasinonlocal coupling; finite deformations; sharp stability; error analysis
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Funding
- EPSRC
- EPSRC [EP/H003096/1] Funding Source: UKRI
- Engineering and Physical Sciences Research Council [EP/H003096/1] Funding Source: researchfish
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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 consistency error estimates in negative norms, novel a priori and a posteriori stability estimates, and a quantitative inverse function theorem.
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