S. Prudhomme, P. T. Bauman and J. T. Oden
International Journal for Multiscale Computational Engineering, 4, 647–662 (2006).
In this paper, we present an extension of goal-oriented error estimation and adaptation to the simulation of multiscale problems of molecular statics. Computable error estimates for the quasicontinuum method arc developed with respect to specific quantities of interest, and an adaptive strategy based on these estimates is proposed for error control. The theoretical results are illustrated on a nanoindentation problem in which the quantity of interest is the force acting on the indenter. The promising capability of such error estimates and adaptive procedure for the solution of multiscale problems is demonstrated on numerical examples.