On principles for the selection of shape functions for the Generalized Finite Element Method

Ivo Babuška; Uday Banerjee; John E. Osborn

doi:10.1016/S0045-7825(02)00467-X

On principles for the selection of shape functions for the Generalized Finite Element Method

Ivo Babuška, Uday Banerjee, John E. Osborn

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

43 Scopus citations

Abstract

Effective shape functions for the Generalized Finite Element Method should reflect the available information on the solution. This information is partially fuzzy, because the solution is, of course, unknown, and typically the only available information is the solution's inclusion in a variety of function spaces. It is desirable to choose shape functions that perform robustly over a family of relevant situations. Quantitative notions of robustness are introduced and discussed. We show, in particular, that in one dimension polynomials are robust when the available information consists in inclusions in Sobolev-type spaces that are x-independent.

Original language	English (US)
Pages (from-to)	5595-5629
Number of pages	35
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	191
Issue number	49-50
DOIs	https://doi.org/10.1016/S0045-7825(02)00467-X
State	Published - Dec 6 2002

Keywords

Algebraic polynomials
Approximations
Error estimates
Galerkin methods
Generalized finite element methods
Sup-inf
Trigonometric polynomials
n-widths

ASJC Scopus subject areas

Computational Mechanics
Mechanics of Materials
Mechanical Engineering
General Physics and Astronomy
Computer Science Applications

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10.1016/S0045-7825(02)00467-X

Cite this

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title = "On principles for the selection of shape functions for the Generalized Finite Element Method",

abstract = "Effective shape functions for the Generalized Finite Element Method should reflect the available information on the solution. This information is partially fuzzy, because the solution is, of course, unknown, and typically the only available information is the solution's inclusion in a variety of function spaces. It is desirable to choose shape functions that perform robustly over a family of relevant situations. Quantitative notions of robustness are introduced and discussed. We show, in particular, that in one dimension polynomials are robust when the available information consists in inclusions in Sobolev-type spaces that are x-independent.",

keywords = "Algebraic polynomials, Approximations, Error estimates, Galerkin methods, Generalized finite element methods, Sup-inf, Trigonometric polynomials, n-widths",

author = "Ivo Babu{\v s}ka and Uday Banerjee and Osborn, {John E.}",

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AU - Babuška, Ivo

AU - Banerjee, Uday

AU - Osborn, John E.

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N2 - Effective shape functions for the Generalized Finite Element Method should reflect the available information on the solution. This information is partially fuzzy, because the solution is, of course, unknown, and typically the only available information is the solution's inclusion in a variety of function spaces. It is desirable to choose shape functions that perform robustly over a family of relevant situations. Quantitative notions of robustness are introduced and discussed. We show, in particular, that in one dimension polynomials are robust when the available information consists in inclusions in Sobolev-type spaces that are x-independent.

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KW - Algebraic polynomials

KW - Approximations

KW - Error estimates

KW - Galerkin methods

KW - Generalized finite element methods

KW - Sup-inf

KW - Trigonometric polynomials

KW - n-widths

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On principles for the selection of shape functions for the Generalized Finite Element Method

Abstract

Keywords

ASJC Scopus subject areas

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