TY - GEN

T1 - From a Geometrical Interpretation of Bramble-Hilbert Lemma to a Probability Distribution for Finite Element Accuracy

AU - Chaskalovic, Joel

AU - Assous, Franck

N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Bramble-Hilbert lemma

KW - Error estimates

KW - Finite elements

KW - Probability

UR - http://www.scopus.com/inward/record.url?scp=85066140353&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11539-5_1

DO - 10.1007/978-3-030-11539-5_1

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AN - SCOPUS:85066140353

SN - 9783030115388

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 3

EP - 14

BT - Finite Difference Methods. Theory and Applications - 7th International Conference, FDM 2018, Revised Selected Papers

A2 - Dimov, Ivan

A2 - Faragó, István

A2 - Vulkov, Lubin

T2 - 7th International Conference on Finite Difference Methods, FDM 2018

Y2 - 11 June 2018 through 16 June 2018

ER -