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 journalArticlepeer-review

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 for computing such equilibria. The estimates are derived in a W1,∞ 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
Externally publishedYes

Keywords

  • A priori and a posteriori analysis
  • Multilattice
  • Multiscale method
  • Quasicontinuum method

Fingerprint

Dive into the research topics of 'A priori and a posteriori W1,∞ error analysis of a QC method for complex lattices'. Together they form a unique fingerprint.

Cite this