In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well and states new issues, here tackled, concerning good quality mesh elements and reliability of the simulations. In this paper we numerically investigate optimality with respect to the number of degrees of freedom of the numerical solutions obtained by the different refinement strategies proposed. A geometrically complex geophysical problem is used as test problem for several general purpose and problem dependent refinement strategies.

中文翻译：

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应用于自适应 VEM 离散化的多边形网格细化策略

在复杂几何域上的微分问题的离散化中，基于多边形和多面体元素的离散化方法是强有力的工具。针对此类问题的自适应网格细化也非常有用，并说明了此处解决的新问题，涉及高质量的网格元素和模拟的可靠性。在本文中，我们对通过提出的不同细化策略获得的数值解的自由度数进行数值研究。几何复杂的地球物理问题被用作几个通用目的和问题相关的细化策略的测试问题。