Indeterminate Constants in Numerical Approximations of PDEs: A Pilot Study Using Data Mining Techniques - Archive ouverte HAL Access content directly
Journal Articles Journal of Computational and Applied Mathematics Year : 2014

Indeterminate Constants in Numerical Approximations of PDEs: A Pilot Study Using Data Mining Techniques

, (1)
1
Franck Assous
  • Function : Author
Joël Chaskalovic
  • Function : Author
  • PersonId : 1209721

Abstract

Rolle's theorem, and therefore, Lagrange and Taylor's theorems are responsible for the inability to determine precisely the error estimate of numerical methods applied to partial differential equations. Basically, this comes from the existence of a non unique unknown point which appears in the remainder of Taylor's expansion. In this paper we consider the case of finite elements method. We show in details how Taylor's theorem gives rise to indeterminate constants in the a priori error estimates. As a consequence, we highlight that classical conclusions have to be reformulated if one considers local error estimate. To illustrate our purpose, we consider the implementation of P1 and P2 finite elements method to solve Vlasov-Maxwell equations in a paraxial configuration. If Bramble-Hilbert theorem claims thatglobal error estimates for finite elements P2 are "better " than the P1 ones, we show how data mining techniques are powerful to identify and to qualify when and where local numerical results of P1 and P2 are equivalent.
Fichier principal
Vignette du fichier
JCAM 2014.pdf (388.87 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03913566 , version 1 (27-12-2022)

Identifiers

Cite

Franck Assous, Joël Chaskalovic. Indeterminate Constants in Numerical Approximations of PDEs: A Pilot Study Using Data Mining Techniques. Journal of Computational and Applied Mathematics, 2014, 270, pp.462-470. ⟨10.1016/j.cam.2013.12.015⟩. ⟨hal-03913566⟩
0 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More