The virtual element method on image-based domain approximations

We analyze and validate the virtual element method combined with a projection approach similar to the one in [1, 2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains obtained as the union of squared elements out of a uniform structured mesh, such as the one that naturally arise when the domain is issued from an image. We show, both theoretically and numerically, that resorting to the use of polygonal element allows to satisfy the assumptions required for the stability of the projection approach, thus allowing to fully exploit the potential of higher order methods, which makes the resulting approach an effective alternative to the use of the finite element method.