The present review paper has several objectives. Its primary aim is to give an idea of the general features of virtual element methods (VEMs), which were introduced about a decade ago in the field of numerical methods for partial differential equations, in order to allow decompositions of the computational domain into polygons or polyhedra of a very general shape.Nonetheless, the paper is also addressed to readers who have already heard (and possibly read) about VEMs and are interested in gaining more precise information, in particular concerning their application in specific subfields such as ${C}^1$ -approximations of plate bending problems or approximations to problems in solid and fluid mechanics.

中文翻译：

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虚元法

本审查文件有几个目标。它的主要目的是让人们了解大约十年前在偏微分方程数值方法领域引入的虚元法 (VEM) 的一般特征，以便将计算域分解为多边形或非常一般形状的多面体。尽管如此，本文还面向已经听说过（并可能阅读过）VEM 并且有兴趣获得更精确信息的读者，特别是关于它们在特定子领域的应用，例如${C}^1$- 板弯曲问题的近似值或固体和流体力学问题的近似值。