An error-estimate-free and remapping-free variational mesh refinement and coarsening method for dissipative solids at finite strains

2009 ◽  
Vol 77 (3) ◽  
pp. 437-450 ◽  
Author(s):  
J. Mosler ◽  
M. Ortiz
Keyword(s):  
Error Estimate ◽  
Mesh Refinement ◽  
Finite Strains

On generalized binomial laws to evaluate finite element accuracy: preliminary probabilistic results for adaptive mesh refinement

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
Joël Chaskalovic ◽  
Franck Assous
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Error Estimate ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Random Variable ◽  
Geometrical Interpretation ◽  
Relative Accuracy ◽  
Probabilistic Methods

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.

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