author = {Conti, Sergio and Geihe, Benedict and Lenz, Martin and Rumpf, Martin},
  title = {A posteriori modeling error estimates in the optimization of two-scale
	elastic composite materials},
  journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
  year = {2017},
  note = {to appear},
  abstract = {The a posteriori analysis of the discretization error and the modeling
	error is studied for a compliance cost functional in the context
	of the optimization of composite elastic materials and a two-scale
	linearized elasticity model. A mechanically simple, parametrized
	microscopic supporting structure is chosen and the parameters describing
	the structure are determined minimizing the compliance objective.
	An a posteriori error estimate is derived which includes the modeling
	error caused by the replacement of a nested laminate microstructure
	by this considerably simpler microstructure. Indeed, nested laminates
	are known to realize the minimal compliance and provide a benchmark
	for the quality of the microstructures. To estimate the local difference
	in the compliance functional the dual weighted residual approach
	is used. Different numerical experiments show that the resulting
	adaptive scheme leads to simple parametrized microscopic supporting
	structures that can compete with the optimal nested laminate construction.
	The derived a posteriori error indicators allow to verify that the
	suggested simplified microstructures achieve the optimal value of
	the compliance up to a few percent. Furthermore, it is shown how
	discretization error and modeling error can be balanced by choosing
	an optimal level of grid refinement. Our two scale results with a
	single scale microstructure can provide guidance towards the design
	of a producible macroscopic fine scale pattern.},
  eprint = {1511.04329},
  pdf = { 1},