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 "good" simplices. A numerical experiment confirms the theoretical result.

翻译：在泊松方程有限元解的误差估计中，通常需要对所使用的网格施加形状正则性假设。本文证明，即使违背形状正则性条件，只要"坏"单元（违背形状正则性或最大角条件的单元）能被"好"单纯形虚拟覆盖，仍可获得标准误差估计。数值实验验证了该理论结果。