  A virtual element discretisation of an Arbitrary Lagrangian-Eulerian method
for two-dimensional convection-diffusion equations is proposed employing an
isoparametric Virtual Element Method to achieve higher-order convergence rates
on curved edged polygonal meshes. The proposed method is validated with
numerical experiments in which optimal $H^1$ and $L^2$ convergence are
observed. This method is then successfully applied to an existing moving mesh
algorithm for implicit moving boundary problems in which higher-order
convergence is achieved.
