## 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.

Original language | English |
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Title of host publication | Finite Difference Methods. Theory and Applications - 7th International Conference, FDM 2018, Revised Selected Papers |

Editors | Ivan Dimov, István Faragó, Lubin Vulkov |

Publisher | Springer Verlag |

Pages | 3-14 |

Number of pages | 12 |

ISBN (Print) | 9783030115388 |

DOIs | |

State | Published - 2019 |

Externally published | Yes |

Event | 7th International Conference on Finite Difference Methods, FDM 2018 - Lozenetz, Bulgaria Duration: 11 Jun 2018 → 16 Jun 2018 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 11386 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th International Conference on Finite Difference Methods, FDM 2018 |
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Country/Territory | Bulgaria |

City | Lozenetz |

Period | 11/06/18 → 16/06/18 |

### Bibliographical note

Publisher Copyright:© 2019, Springer Nature Switzerland AG.

## Keywords

- Bramble-Hilbert lemma
- Error estimates
- Finite elements
- Probability