author = {Geihe, Benedict and Rumpf, Martin},
  title = {A posteriori error estimates for sequential laminates in shape optimization},
  journal = {Discrete and Continuous Dynamical Systems - Series S},
  year = {2016},
  volume = {9},
  pages = {1377--1392},
  number = {5},
  abstract = {Abstract A posteriori error estimates are derived in the context of
	two-dimensional structural elastic shape optimization under the compliance
	objective. It is known that the optimal shape features are microstructures
	that can be constructed using sequential lamination. The descriptive
	parameters explicitly depend on the stress. To derive error estimates
	the dual weighted residual approach for control problems in PDE constrained
	optimization is employed, involving the elastic solution and the
	microstructure parameters. Rigorous estimation of interpolation errors
	ensures robustness of the estimates while local approximations are
	used to obtain fully practical error indicators. Numerical results
	show sharply resolved interfaces between regions of full and intermediate
	material density.},
  doi = {10.3934/dcdss.2016055},
  eprint = {1501.07461},
  pdf = { 1},
  issn = {1937-1632},
  url = {}