In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In particular, we consider only star-shaped polygons for the meshes. Suitable error estimates are presented, where a rigorous analysis on the influence of the Lam\'e constants in each estimate is presented. We report numerical tests to assess the performance of the method.

翻译：本文分析了一种允许小边的二维弹性问题的虚拟元方法。通过该方法，可放宽对多边形网格几何特征的传统假设。具体而言，我们仅考虑星形多边形网格。文中给出了恰当的误差估计，并严格分析了拉梅常数对每个估计的影响。我们报告了数值实验以评估该方法的性能。