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

Assyr Abdulle, Ping Lin, Alexander V. Shapeev

    Research output: Contribution to journalArticle

    5 Citations (Scopus)

    Abstract

    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
    Volume51
    Issue number4
    DOIs
    Publication statusPublished - 2013

    Fingerprint Dive into the research topics of 'A priori and a posteriori <em>W</em><sup>1,</sup>∞error analysis of a QC method for complex lattices'. Together they form a unique fingerprint.

  • Cite this