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A new probabilistic interpretation of Bramble-Hilbert lemma. (arXiv:1803.09547v2 [math.NA] UPDATED)
来源于:arXiv
The aim of this paper is to provide new perspectives on relative finite
element accuracy which is usually based on the asymptotic speed of convergence
comparison when the mesh size $h$ goes to zero. Starting from a geometrical
reading of the error estimate due to Bramble-Hilbert lemma, we derive two
probability distributions that estimate the relative accuracy, considered as a
random variable, between two Lagrange finite elements $P_k$ and $P_m$, ($k <
m$). We establish mathematical properties of these probabilistic distributions
and we get new insights which, among others, show that $P_k$ or $P_m$ is more
likely accurate than the other, depending on the value of the mesh size $h$. 查看全文>>