On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement
Keyword(s):
AbstractThe aim of this paper is to provide new perspectives on the relative finite elements accuracy. Starting from a geometrical interpretation of the error estimate which can be deduced from Bramble–Hilbert lemma, we derive a probability law that evaluates the relative accuracy, considered as a random variable, between two finite elements Pk and Pm, k < m. We extend this probability law to get a cumulated probabilistic law for two main applications. The first one concerns a family of meshes, the second one is dedicated to a sequence of simplexes constituting a given mesh. Both of these applications could be considered as a first step toward application for adaptive mesh refinement with probabilistic methods.
2020 ◽
Vol 20
(4)
◽
pp. 799-813
Keyword(s):
2019 ◽
Vol 121
(4)
◽
pp. 588-601
◽
1987 ◽
Vol 53
(491)
◽
pp. 1388-1392
◽
2005 ◽
Vol 41
(15)
◽
pp. 1413-1440
◽
Keyword(s):
Keyword(s):
1990 ◽
Vol 26
(5)
◽
pp. 2187-2189
◽
Keyword(s):
1990 ◽
Vol 30
(3)
◽
pp. 473-489
◽
Keyword(s):
2021 ◽
2001 ◽
pp. 266-276
◽
Keyword(s):