A priori and a posteriori W^1,∞error analysis of a QC method for complex lattices

TY - JOUR

T1 - A priori and a posteriori W1,∞error analysis of a QC method for complex lattices

AU - Abdulle, Assyr

AU - Lin, Ping

AU - Shapeev, Alexander V.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

U2 - 10.1137/120894300

DO - 10.1137/120894300

M3 - Article

SN - 0036-1429

VL - 51

SP - 2357

EP - 2379

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 4

ER -