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.

翻译：针对二维对流扩散方程，本文提出一种基于任意拉格朗日-欧拉方法的虚拟单元离散格式。该格式采用等参虚拟单元法，在曲边多边形网格上实现高阶收敛速率。数值实验验证了所提方法的有效性，观察到最优的$H^1$和$L^2$收敛性。该方法随后被成功应用于现有隐式移动边界问题的移动网格算法中，实现了高阶收敛。