论文标题
概率定律的数值验证以评估有限元误差估计值
Numerical validation of probabilistic laws to evaluate finite element error estimates
论文作者
论文摘要
我们提出了一种应用概率方法的数值验证，用于估计两个Lagrange有限元素$ p_k $和$ p_m（k <m）$之间的相对准确性。特别是，我们显示有限元$ p_ {k} $比有限元$ p_ {m {m} $更准确的结果。这说明了我们最近得出的理论概率框架，以评估实际准确性。这也强调了比较两种数值方法时所需的额外谨慎的重要性，因为错误估计的经典结果仅涉及渐近收敛率。
We propose a numerical validation of a probabilistic approach applied to estimate the relative accuracy between two Lagrange finite elements $P_k$ and $P_m, (k<m)$. In particular, we show practical cases where finite element $P_{k}$ gives more accurate results than finite element $P_{m}$. This illustrates the theoretical probabilistic framework we recently derived in order to evaluate the actual accuracy. This also highlights the importance of the extra caution required when comparing two numerical methods, since the classical results of error estimates concerns only the asymptotic convergence rate.
