  We propose a method to modify a polygonal mesh in order to fit the
zero-isoline of a level set function by extending a standard body-fitted
strategy to a tessellation with arbitrarily-shaped elements. The novel level
set-fitted approach, in combination with a Discontinuous Galerkin finite
element approximation, provides an ideal setting to model physical problems
characterized by embedded or evolving complex geometries, since it allows
skipping any mesh post-processing in terms of grid quality. The proposed
methodology is firstly assessed on the linear elasticity equation, by verifying
the approximation capability of the level set-fitted approach when dealing with
configurations with heterogeneous material properties. Successively, we combine
the level set-fitted methodology with a minimum compliance topology
optimization technique, in order to deliver optimized layouts exhibiting crisp
boundaries and reliable mechanical performances. An extensive numerical test
campaign confirms the effectiveness of the proposed method.
