Estimating and localizing the algebraic and total numerical errors using flux reconstructions - Archive ouverte HAL Access content directly
Journal Articles Numerische Mathematik Year : 2018

Estimating and localizing the algebraic and total numerical errors using flux reconstructions

(1, 2) , (1) , (3, 4)
1
2
3
4

Abstract

This paper presents a methodology for computing upper and lower bounds for both the algebraic and total errors in the context of the conforming finite element discretization and an arbitrary iterative algebraic solver. The derived bounds are based on the flux reconstruction techniques, do not contain any unspecified constants, and allow estimating the local distribution of both errors over the computational domain. We also discuss bounds on the discretization error, their application for constructing mathematically justified stopping criteria for iterative algebraic solvers, global and local efficiency of the total error upper bound, and the relationship to the previously published estimates on the algebraic error. Theoretical results are illustrated on numerical experiments for higher-order finite element approximations and the preconditioned conjugate gradient method. They in particular witness that the proposed methodology yields a tight estimate on the local distribution of the algebraic and total errors over thecomputational domain and illustrate the associate cost.
Fichier principal
Vignette du fichier
PapStrVoh18_HAL.pdf (3.39 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01312430 , version 1 (06-05-2016)
hal-01312430 , version 2 (20-04-2018)

Identifiers

Cite

Jan Papež, Zdeněk Strakoš, Martin Vohralík. Estimating and localizing the algebraic and total numerical errors using flux reconstructions. Numerische Mathematik, 2018, 138 (3), pp.681-721. ⟨10.1007/s00211-017-0915-5⟩. ⟨hal-01312430v2⟩
350 View
291 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More