A priori and a posteriori W1,∞error analysis of a QC method for complex lattices

Assyr Abdulle, Ping Lin, Alexander V. Shapeev

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    5 Citations (Scopus)


    In this paper we derive regularity results for equilibria of multilattices under an
    external force and prove a priori and a posteriori error estimates for a multiscale numerical method forcomputing such equilibria. The estimates are derived in a W1,8 norm in one space dimension. One of the features of our analysis is that we establish an equivalent way of formulating the coarse-grained problem which greatly simplifies derivation of the error bounds (both a priori and a posteriori). We
    illustrate our error estimates with numerical experiments.
    Original languageEnglish
    Pages (from-to)2357-2379
    Number of pages23
    JournalSIAM Journal on Numerical Analysis
    Issue number4
    Publication statusPublished - 2013

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