On Round-off Error for Adaptive Finite Element Methods

被引：8

作者：

Alvarez-Aramberri, J. ^{[1
]}

Pardo, D. ^{[1
,2
]}

Paszynski, Maciej ^{[3
]}

Collier, Nathan ^{[4
]}

Dalcin, Lisandro ^{[5
]}

Calo, Victor M. ^{[4
]}

机构：

[1] Univ Basque Country UPV EHU, Dept Appl Math Stat & Operat Res, Bilbao, Spain

[2] Ikerbasque, Bilbao, Spain

[3] AGH Univ Sci & Technol, Krakow, Poland

[4] King Abdullah Univ Sci & Technol KAUST, Riyadh, Saudi Arabia

[5] Consejo Nacl Invest Cient & Tecn, Santa Fe, Argentina

来源：

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON COMPUTATIONAL SCIENCE, ICCS 2012 | 2012年 / 9卷

关键词：

Finite Element Methods (FEM); hp-adaptivity; round-off error; condition number;

D O I：

10.1016/j.procs.2012.04.162

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

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.

引用

页码：1474 / 1483

页数：10

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