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.

翻译：虚拟元件方法用于计算网格速度和在普通多边形网外的保守的Lagrangian-Eulerian解决方案传输。该方法将线性限量元素方法扩大到多边形网格结构,达到同样的精确度。在移动网目方面,虚拟元件方法的一个主要优点是可以在网目边缘插入节点的方便度。 节点插入技术的演示显示,移动多边形网目可以简单地适应边界遇到固物体或另一个移动边界的情况,而不会降低准确度。