A priori and a posteriori \(W^{1,\infty}\) error analysis of a QC method for complex lattices (Q2855111)
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scientific article; zbMATH DE number 6219407
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A priori and a posteriori \(W^{1,\infty}\) error analysis of a QC method for complex lattices |
scientific article; zbMATH DE number 6219407 |
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24 October 2013
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a priori and a posteriori error analysis
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multilattice
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quasicontinuum method
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multiscale method
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equilibrium
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atomistic crystalline material
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convergence
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inf-sup condition
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numerical results
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0.8573168
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0.84292924
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0.8412581
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0.83906937
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0.8385731
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0.8373684
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0.8369194
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A priori and a posteriori \(W^{1,\infty}\) error analysis of a QC method for complex lattices (English)
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The paper is concerned with a problem of equilibrium of an atomistic crystalline material with a complex lattice structure. The regularity results obtained in this paper do not require a high regularity of the external forces. Another feature of the present work is the use of the \(\Gamma\)-convergence theory, which is an useful tool for finding the effective macroscopic energy from the microscopic interaction law, but does not yield the rates of convergence of the minimizers of the microscopic model and the homogenized model. The main contributions can be summarized as follows: (i) the \(\inf\)-\(\sup\) condition and the regularity for the atomistic and homogenized equations; (ii) the convergence of the approximate solutions to the exact ones; (iii) numerical results to support the abstract results of the paper.
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