The estimation of truncation error by tau-estimation revisited

Fraysse, François and Vicente Buendia, Javier de and Valero Sánchez, Eusebio (2011). The estimation of truncation error by tau-estimation revisited. "Journal of Computational Physics", v. 231 (n. 9); pp. 3457-3482. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2011.09.031.

Description

Title: The estimation of truncation error by tau-estimation revisited
Author/s:
  • Fraysse, François
  • Vicente Buendia, Javier de
  • Valero Sánchez, Eusebio
Item Type: Article
Título de Revista/Publicación: Journal of Computational Physics
Date: May 2011
ISSN: 0021-9991
Volume: 231
Subjects:
Freetext Keywords: Truncation error; Finite volume solvers; Multigrid; Uncertainty estimator
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the @t-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error.

More information

Item ID: 12259
DC Identifier: http://oa.upm.es/12259/
OAI Identifier: oai:oa.upm.es:12259
DOI: 10.1016/j.jcp.2011.09.031
Official URL: http://www.sciencedirect.com/science/article/pii/S0021999111006887
Deposited by: Memoria Investigacion
Deposited on: 05 Sep 2012 11:51
Last Modified: 21 Apr 2016 11:30
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