In an error estimation of finite element solutions to the Poisson equation, we usually impose the shape regularity assumption on the meshes to be used. In this paper, we show that even if the shape regularity condition is violated, the standard error estimation can be obtained if "bad" elements elements that violate the shape regularity or maximum angle condition are covered virtually by simplices that satisfy the minimum angle condition. A numerical experiment illustrates the theoretical result.

翻译：在泊松方程有限元解的误差估计中，我们通常对所用网格施加形状正则性假设。本文证明，即使违反形状正则性条件，只要违反形状正则性或最大角条件的"不良"单元能被满足最小角条件的单纯形虚拟覆盖，仍可获得标准误差估计。数值实验验证了理论结果。