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From a Geometrical Interpretation of Bramble-Hilbert Lemma to a Probability Distribution for Finite Element Accuracy

  • Joel ChaskalovicEmail author
  • Franck Assous
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

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.

Keywords

Error estimates Finite elements Bramble-Hilbert lemma Probability 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.∂’alembertSorbonne UniversityParisFrance
  2. 2.Department of MathematicsAriel UniversityArielIsrael

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