We revisit classical Virtual Element approximations on polygonal and polyhedral decompositions. We also recall the treatment proposed for dealing with decompositions into polygons with curved edges. In the second part of the paper we introduce a couple of new ideas for the construction of VEM-approximations on domains with curved boundary, both in two and three dimensions. The new approach looks promising, although sound numerical tests should be made to validate the efficiency of the method.

翻译：本文重新审视了多边和多面体分解上的经典虚拟单元近似方法。同时回顾了处理带有曲边多边形分解的已有方案。在论文第二部分，我们提出了若干新思路，用于在二维和三维空间中构建具有弯曲边界的域上的VEM近似方法。这一新方法前景可观，但仍需进行可靠的数值测试以验证其有效性。