Observations on the numerical stability of the Galerkin method |
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Authors: | Dallas Allan G Hsiao GC Kleinman RE |
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Institution: | (1) Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA |
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Abstract: | 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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | |
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