  We present a velocity-based moving mesh virtual element method for the
numerical solution of PDEs involving moving boundaries. The virtual element
method is used for computing both the mesh velocity and a conservative
Arbitrary Lagrangian-Eulerian solution transfer on general polygonal meshes.
The approach extends the linear finite element method to polygonal mesh
structures, achieving the same degree of accuracy. In the context of moving
meshes, a major advantage of the virtual element approach is the ease with
which nodes can be inserted on mesh edges. Demonstrations of node insertion
techniques are presented to show that moving polygonal meshes can be simply
adapted for situations where a boundary encounters a solid object or another
moving boundary, without reduction in degree of accuracy.
