Many practical problems occur due to the boundary value problem. This paper evaluates the finite element solution of the boundary value problem of Poisson's equation and proposes a novel a posteriori local error estimation based on the Hypercircle method. Compared to the existing literature on qualitative error estimation, the proposed error estimation provides an explicit and sharp bound for the approximation error in the subdomain of interest and is applicable to problems without the $H^2$ regularity. The efficiency of the proposed method is demonstrated by numerical experiments for both convex and non-convex 2D domains.

翻译：许多实际问题都是由于边界价值问题造成的。本文件评估了Poisson方程式边界价值问题的有限要素解决方案,并提出了基于超圆环法的新的事后局部误差估计。与关于质量误差估计的现有文献相比,拟议的误差估计为利益次域近似误差提供了明确和尖锐的界限,并适用于没有$H2美元规律的问题。对convex和非convex 2D 域的数值实验证明了拟议方法的效率。