A priori and a posteriori $W^{1,\infty}$ error analysis of a QC method for complex lattices

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 W-1,W-infinity 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.


Published in:
SIAM, Journal on Numerical Analysis, 51, 4, 2357-2379
Year:
2013
Publisher:
Philadelphia, Siam Publications
Keywords:
Laboratories:




 Record created 2012-11-07, last modified 2018-03-17

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