  We study the finite element approximation of the solid isotropic material
with penalization (SIMP) model for the topology optimization problem of
minimizing the compliance of a linearly elastic structure. To ensure the
existence of a local minimizer to the infinite-dimensional problem, we consider
two popular regularization methods: $W^{1,p}$-type penalty methods and density
filtering. Previous results prove weak(-*) convergence in the space of the
material distribution to a local minimizer of the infinite-dimensional problem.
Notably, convergence was not guaranteed to \emph{all} the isolated local
minimizers. In this work, we show that, for every isolated local or global
minimizer, there exists a sequence of finite element local minimizers that
strongly converges to the minimizer in the appropriate space. As a by-product,
this ensures that there exists a sequence of unfiltered discretized material
distributions that does not exhibit checkerboarding.
