On Round-off Error for Adaptive Finite Element Methods

J. Alvarez-Aramberri, David Pardo, Maciej Paszynski, Nathan Collier, Lisandro Dalcin, Victor M. Calo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.
Original languageEnglish (US)
Title of host publicationProcedia Computer Science
PublisherElsevier BV
Pages1474-1483
Number of pages10
DOIs
StatePublished - Jun 2 2012

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