  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.
