NDLI: Computable Pointwise Error Bounds and the Ritz Method in One Dimension

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Gartland, Jr., E. C.
Copyright Year	1984
Abstract	This paper is concerned with a posteriors error estimation for the numerical approximation, by the Ritz method, of linear, selfadjoint, two-point boundary value problems. The point of departure is a basic inequality, which is the best possible (given the information used in computing the approximation), that bounds the pointwise error in the Ritz approximation. This optimal bound involves some readily available information and some quantities (functionals of the true solution and Greens function) that are not, in general, known. The problem of estimating these latter quantities, and thus producing computable bounds, is approached from two different points of view; first, using complementary variational principles, and second, approximating the energy inner product and using the theory of kernel functions. Numerical results are given, and possible extensions to higher dimensions are commented on.
Starting Page	84
Ending Page	100
Page Count	17
File Format	PDF
ISSN	00361429
DOI	10.1137/0721005
e-ISSN	10957170
Issue Number	1
Volume Number	21
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-17
Access Restriction	Subscribed
Subject Keyword	Boundary value problems Finite elements, Rayleigh-Ritz, Galerkin and collocation methods Mesh generation and refinement Ritz method two-point boundary value problems a posteriors error estimation
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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