On Round-off Error for Adaptive Finite Element Methods | Zendy

J. Álvarez-Aramberri | Zendy; David Pardo | Zendy; Maciej Paszyński | Zendy; Nathan Collier | Zendy; Lisandro Dalcín | Zendy; Victor M. Calo | Zendy

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On Round-off Error for Adaptive Finite Element Methods

Author(s) -

J. Álvarez-Aramberri,

David Pardo,

Maciej Paszyński,

Nathan Collier,

Lisandro Dalcín,

Victor M. Calo

Publication year - 2012

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2012.04.162

Subject(s) - computer science , finite element method , polygon mesh , condition number , context (archaeology) , matrix (chemical analysis) , error analysis , poisson's equation , mathematics , error detection and correction , algorithm , poisson distribution , element (criminal law) , boundary value problem , mathematical optimization , mathematical analysis , eigenvalues and eigenvectors , statistics , paleontology , physics , computer graphics (images) , materials science , quantum mechanics , biology , composite material , thermodynamics , political science , law

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

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