Observations on the numerical stability of the Galerkin method

被引：10

作者：

Dallas, AG ^{[1
]}

Hsiao, GC ^{[1
]}

Kleinman, RE ^{[1
]}

机构：

[1] Univ Delaware, Dept Math Sci, Newark, DE 19716 USA

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 1998年 / 9卷 / 1-2期

关键词：

D O I：

10.1023/A:1018941607627

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

A simple factorization of the finite-dimensional Galerkin operators motivates a study of the numerical stability of a Galerkin procedure on the basis of its "potential stability" and the "conditioning" of its coordinate functions. Conditions sufficient for stability and conditions leading to instability are thereby identified. Numerical examples of stability and instability occurring in the application of the Galerkin method to boundary-integral equations arising in simple scattering problems are provided and discussed within this framework. Numerical instabilities reported by other authors are examined and explained from the same point of view.

引用

页码：37 / 67

页数：31

共 16 条

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[2]

Aubin J.-P., 1972, APPROXIMATION ELLIPT

[3]

Braess D., 1997, FINITE ELEMENTS

[4]

DALLAS AG, 1987, 9008 NRL