论文标题
应用于有限元误差近似的广义beta质量分布
Generalized Beta Prime Distribution Applied to Finite Element Error Approximation
论文作者
论文摘要
在本文中，我们提出了基于广义beta Prime分布的新一代概率定律，以估计两个Lagrange有限元素之间的相对准确性$ P_ {K_1} $和$ P_ {K_2}，（K_1 <k_2）$。由于相对有限元的精度通常基于当网格尺寸$ h $变为零时的渐近速度的比较，因此该概率定律强调存在，具体取决于$ h $，因此，$ p_ {k_1} $有限元的可能性比$ p_ p_ p_ {k_2} $更准确。为了确认此功能，我们在实际示例中显示和检查，统计频率之间的拟合质量以及概率定律确定的相应概率。除其他外，当$ h $从零移动时，有限元素$ p_ {k_1} $可能会产生比有限元$ p_ {k_2} $更精确的结果，因为事件的可能性“ $ p_ {k_1} $比$ p_ p_ {k_2} $更准确，而不是0.5。在这些情况下，$ p_ {k_2} $有限元素更有可能获得资格过高。
In this paper we propose a new generation of probability laws based on the generalized Beta prime distribution to estimate the relative accuracy between two Lagrange finite elements $P_{k_1}$ and $P_{k_2}, (k_1<k_2)$. Since the relative finite element accuracy is usually based on the comparison of the asymptotic speed of convergence when the mesh size $h$ goes to zero, this probability laws highlight that there exists, depending on $h$, cases such that $P_{k_1}$ finite element is more likely accurate than the $P_{k_2}$ one. To confirm this feature, we show and examine on practical examples, the quality of the fit between the statistical frequencies and the corresponding probabilities determined by the probability law. Among others, it validates, when $h$ moves away from zero, that finite element $P_{k_1}$ may produces more precise results than a finite element $P_{k_2}$ since the probability of the event "$P_{k_1}$ is more accurate than $P_{k_2}$" consequently increases to become greater than 0.5. In these cases, $P_{k_2}$ finite elements are more likely overqualified.
