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:在本文中,我们分析了允许小边缘的两维弹性问题的一种虚拟元素方法。 采用这种方法, 多边形藻类几何特征的经典假设可以放松。 特别是, 我们只考虑对藻类只使用恒星形多边形。 提出了合适的误差估计, 其中对每个估计中Lam\'e常数的影响进行了严格的分析。 我们报告数字测试,以评估方法的性能 。</s>