  The mesh flexibility offered by the virtual element method through the
permission of arbitrary element geometries, and the seamless incorporation of
`hanging' nodes, has made the method increasingly attractive in the context of
adaptive remeshing. There exists a healthy literature concerning error
estimation and adaptive refinement techniques for virtual elements while the
topic of adaptive coarsening (i.e. de-refinement) is in its infancy. The
creation of a quasi-optimal mesh is based on the principle of quasi-even error
distribution over the elements which inherently relies on localized refinement
and coarsening techniques. Thus, necessitating a fully adaptive remeshing
procedure. In this work a novel fully adaptive remeshing procedure for the
virtual element method is presented. Additionally, novel procedures are
proposed for the identification of elements qualifying for refinement or
coarsening based on user-defined targets. Specifically, a target percentage
error, target number of elements, or target number of nodes can be selected.
Numerical results demonstrate that the adaptive remeshing procedure can meet
any prescribed target while creating a quasi-optimal mesh. The proposed fully
adaptive procedure is of particular interest in engineering applications
requiring an efficient simulation of a given accuracy, or desiring a simulation
with the maximum possible accuracy for a given computational constraint.
