Error estimates for a finite volume method for the Laplace equation in dimension one through discrete Green functions. - Archive ouverte HAL Access content directly
Journal Articles International Journal on Finite Volumes Year : 2009

Error estimates for a finite volume method for the Laplace equation in dimension one through discrete Green functions.

(1, 2)
1
2

Abstract

The cell-centered finite volume approximation of the Laplace equation in dimension one is considered. An exact expression of the error between the exact and numerical solutions is derived through the use of continuous and discrete Green functions. This allows to discuss convergence of the method in the L infinity and L2 norms with respect to the choice of the control points in the cells and with respect to the regularity of the data. Well-known second-order convergence results are recovered if those control points are properly chosen and if the data belongs to H1. Counterexamples are constructed to show that second-order may be lost if these conditions are not met.
Fichier principal
Vignette du fichier
IJFVomnes_09.pdf (168.26 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

cea-00391590 , version 1 (04-06-2009)

Identifiers

  • HAL Id : cea-00391590 , version 1

Cite

Pascal Omnes. Error estimates for a finite volume method for the Laplace equation in dimension one through discrete Green functions.. International Journal on Finite Volumes, 2009, 6 (1). ⟨cea-00391590⟩
135 View
167 Download

Share

Gmail Facebook Twitter LinkedIn More